Properties

Label 9200.2.a
Level $9200$
Weight $2$
Character orbit 9200.a
Rep. character $\chi_{9200}(1,\cdot)$
Character field $\Q$
Dimension $209$
Newform subspaces $83$
Sturm bound $2880$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 83 \)
Sturm bound: \(2880\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9200))\).

Total New Old
Modular forms 1476 209 1267
Cusp forms 1405 209 1196
Eisenstein series 71 0 71

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(25\)
\(+\)\(+\)\(-\)\(-\)\(25\)
\(+\)\(-\)\(+\)\(-\)\(27\)
\(+\)\(-\)\(-\)\(+\)\(27\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(25\)
\(-\)\(-\)\(-\)\(-\)\(31\)
Plus space\(+\)\(97\)
Minus space\(-\)\(112\)

Trace form

\( 209 q + 2 q^{3} + 4 q^{7} + 205 q^{9} + O(q^{10}) \) \( 209 q + 2 q^{3} + 4 q^{7} + 205 q^{9} + 2 q^{13} - 6 q^{17} + 4 q^{19} - 3 q^{23} + 2 q^{27} + 2 q^{29} + 22 q^{31} + 8 q^{33} + 10 q^{37} - 18 q^{39} + 2 q^{41} + 32 q^{43} + 2 q^{47} + 225 q^{49} - 44 q^{51} - 6 q^{53} + 8 q^{57} - 8 q^{59} + 2 q^{61} - 40 q^{63} + 16 q^{67} + 6 q^{71} - 6 q^{73} - 8 q^{77} + 52 q^{79} + 201 q^{81} - 20 q^{83} + 10 q^{87} - 14 q^{89} + 60 q^{91} + 12 q^{93} - 14 q^{97} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9200))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 23
9200.2.a.a 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.d \(0\) \(-3\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-6q^{13}+\cdots\)
9200.2.a.b 9200.a 1.a $1$ $73.462$ \(\Q\) None 92.2.a.a \(0\) \(-3\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{7}+6q^{9}-2q^{11}+5q^{13}+\cdots\)
9200.2.a.c 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.a.a \(0\) \(-3\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}-q^{13}+6q^{21}+\cdots\)
9200.2.a.d 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.e.a \(0\) \(-2\) \(0\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-3q^{7}+q^{9}+6q^{13}+7q^{17}+\cdots\)
9200.2.a.e 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.c \(0\) \(-2\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-5q^{11}+7q^{13}+\cdots\)
9200.2.a.f 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.a \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
9200.2.a.g 9200.a 1.a $1$ $73.462$ \(\Q\) None 115.2.b.a \(0\) \(-2\) \(0\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+2q^{13}-5q^{17}+\cdots\)
9200.2.a.h 9200.a 1.a $1$ $73.462$ \(\Q\) None 2300.2.a.b \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
9200.2.a.i 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.c \(0\) \(-2\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
9200.2.a.j 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.d \(0\) \(-2\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
9200.2.a.k 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.e \(0\) \(-1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}-2q^{9}-3q^{11}-2q^{13}+\cdots\)
9200.2.a.l 9200.a 1.a $1$ $73.462$ \(\Q\) None 184.2.a.b \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}-2q^{9}+2q^{11}-7q^{13}+\cdots\)
9200.2.a.m 9200.a 1.a $1$ $73.462$ \(\Q\) None 460.2.a.a \(0\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}+4q^{11}-q^{13}+\cdots\)
9200.2.a.n 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.a.b \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}-2q^{11}+5q^{13}+4q^{17}+\cdots\)
9200.2.a.o 9200.a 1.a $1$ $73.462$ \(\Q\) None 184.2.a.a \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}+4q^{11}+5q^{13}+\cdots\)
9200.2.a.p 9200.a 1.a $1$ $73.462$ \(\Q\) None 46.2.a.a \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
9200.2.a.q 9200.a 1.a $1$ $73.462$ \(\Q\) None 460.2.a.b \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-6q^{11}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.r 9200.a 1.a $1$ $73.462$ \(\Q\) None 575.2.a.c \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}+q^{11}+q^{13}+5q^{19}+\cdots\)
9200.2.a.s 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.b \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}+3q^{11}+3q^{13}+8q^{17}+\cdots\)
9200.2.a.t 9200.a 1.a $1$ $73.462$ \(\Q\) None 115.2.a.a \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}-2q^{11}+2q^{13}-3q^{17}+\cdots\)
9200.2.a.u 9200.a 1.a $1$ $73.462$ \(\Q\) None 575.2.a.c \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+q^{11}-q^{13}+5q^{19}+\cdots\)
9200.2.a.v 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.b \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+3q^{11}-3q^{13}-8q^{17}+\cdots\)
9200.2.a.w 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.a.c \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+6q^{11}+2q^{13}+3q^{17}+\cdots\)
9200.2.a.x 9200.a 1.a $1$ $73.462$ \(\Q\) None 184.2.a.c \(0\) \(0\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}-6q^{11}+2q^{13}-6q^{17}+\cdots\)
9200.2.a.y 9200.a 1.a $1$ $73.462$ \(\Q\) None 460.2.a.c \(0\) \(1\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{7}-2q^{9}+6q^{11}+q^{13}+\cdots\)
9200.2.a.z 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.a.d \(0\) \(1\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}-q^{13}+4q^{17}+\cdots\)
9200.2.a.ba 9200.a 1.a $1$ $73.462$ \(\Q\) None 92.2.a.b \(0\) \(1\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}+q^{13}+6q^{17}+\cdots\)
9200.2.a.bb 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.e \(0\) \(1\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{7}-2q^{9}-3q^{11}+2q^{13}+\cdots\)
9200.2.a.bc 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.d \(0\) \(2\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{7}+q^{9}-5q^{11}+5q^{13}+\cdots\)
9200.2.a.bd 9200.a 1.a $1$ $73.462$ \(\Q\) None 4600.2.a.c \(0\) \(2\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}+5q^{11}+q^{13}+\cdots\)
9200.2.a.be 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.c \(0\) \(2\) \(0\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-5q^{11}-7q^{13}+\cdots\)
9200.2.a.bf 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.a \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
9200.2.a.bg 9200.a 1.a $1$ $73.462$ \(\Q\) None 115.2.b.a \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-2q^{13}+5q^{17}+\cdots\)
9200.2.a.bh 9200.a 1.a $1$ $73.462$ \(\Q\) None 2300.2.a.b \(0\) \(2\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
9200.2.a.bi 9200.a 1.a $1$ $73.462$ \(\Q\) None 920.2.e.a \(0\) \(2\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots\)
9200.2.a.bj 9200.a 1.a $1$ $73.462$ \(\Q\) None 184.2.a.d \(0\) \(3\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{7}+6q^{9}+5q^{13}+6q^{17}+\cdots\)
9200.2.a.bk 9200.a 1.a $1$ $73.462$ \(\Q\) None 460.2.a.d \(0\) \(3\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}+3q^{13}-4q^{17}+\cdots\)
9200.2.a.bl 9200.a 1.a $1$ $73.462$ \(\Q\) None 1150.2.a.d \(0\) \(3\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+6q^{13}+\cdots\)
9200.2.a.bm 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 115.2.a.b \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-1+\beta )q^{7}-2q^{9}+(1+\beta )q^{11}+\cdots\)
9200.2.a.bn 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 4600.2.a.q \(0\) \(-2\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.bo 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 230.2.b.a \(0\) \(-1\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-3+3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bp 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 1150.2.a.k \(0\) \(-1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bq 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 920.2.a.e \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{7}+(1+\beta )q^{9}+2q^{11}+\cdots\)
9200.2.a.br 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 184.2.a.e \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{9}-2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9200.2.a.bs 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{21}) \) None 230.2.a.a \(0\) \(-1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{7}+(2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bt 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 23.2.a.a \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1+\beta )q^{7}+2q^{9}+(3+\beta )q^{11}+\cdots\)
9200.2.a.bu 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 230.2.a.c \(0\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{7}+(-2+\beta )q^{9}+(-2+\cdots)q^{11}+\cdots\)
9200.2.a.bv 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 460.2.a.e \(0\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots\)
9200.2.a.bw 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 1150.2.a.k \(0\) \(1\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
9200.2.a.bx 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{17}) \) None 920.2.a.f \(0\) \(1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
9200.2.a.by 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 230.2.b.a \(0\) \(1\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3-3\beta )q^{7}+(-2+\beta )q^{9}+\cdots\)
9200.2.a.bz 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{5}) \) None 4600.2.a.q \(0\) \(2\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
9200.2.a.ca 9200.a 1.a $2$ $73.462$ \(\Q(\sqrt{13}) \) None 230.2.a.b \(0\) \(3\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
9200.2.a.cb 9200.a 1.a $3$ $73.462$ \(\Q(\zeta_{14})^+\) None 4600.2.a.w \(0\) \(-2\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
9200.2.a.cc 9200.a 1.a $3$ $73.462$ 3.3.321.1 None 2300.2.a.j \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-2\beta _{1}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cd 9200.a 1.a $3$ $73.462$ 3.3.621.1 None 920.2.a.g \(0\) \(0\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{1})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ce 9200.a 1.a $3$ $73.462$ 3.3.2597.1 None 920.2.a.h \(0\) \(1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
9200.2.a.cf 9200.a 1.a $3$ $73.462$ 3.3.1101.1 None 230.2.a.d \(0\) \(1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{7}+(4-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cg 9200.a 1.a $3$ $73.462$ 3.3.321.1 None 2300.2.a.j \(0\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+2\beta _{1}q^{7}+(1-\beta _{1}+\beta _{2})q^{9}+\cdots\)
9200.2.a.ch 9200.a 1.a $3$ $73.462$ \(\Q(\zeta_{14})^+\) None 4600.2.a.w \(0\) \(2\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.ci 9200.a 1.a $3$ $73.462$ 3.3.229.1 None 920.2.a.i \(0\) \(2\) \(0\) \(7\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(2-\beta _{2})q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cj 9200.a 1.a $4$ $73.462$ 4.4.13448.1 None 230.2.b.b \(0\) \(-3\) \(0\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+(-1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.ck 9200.a 1.a $4$ $73.462$ 4.4.5744.1 None 115.2.b.b \(0\) \(-2\) \(0\) \(-6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
9200.2.a.cl 9200.a 1.a $4$ $73.462$ 4.4.15317.1 None 115.2.a.c \(0\) \(-2\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1-\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cm 9200.a 1.a $4$ $73.462$ 4.4.53121.1 None 2300.2.a.l \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cn 9200.a 1.a $4$ $73.462$ 4.4.15529.1 None 4600.2.a.ba \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.co 9200.a 1.a $4$ $73.462$ 4.4.53121.1 None 2300.2.a.l \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cp 9200.a 1.a $4$ $73.462$ 4.4.15529.1 None 4600.2.a.ba \(0\) \(0\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cq 9200.a 1.a $4$ $73.462$ 4.4.5744.1 None 115.2.b.b \(0\) \(2\) \(0\) \(6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2+\beta _{2})q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cr 9200.a 1.a $4$ $73.462$ 4.4.13448.1 None 230.2.b.b \(0\) \(3\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1+\beta _{3})q^{7}+(2+2\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cs 9200.a 1.a $5$ $73.462$ 5.5.791953.1 None 4600.2.a.bc \(0\) \(-3\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
9200.2.a.ct 9200.a 1.a $5$ $73.462$ 5.5.521397.1 None 4600.2.a.bd \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cu 9200.a 1.a $5$ $73.462$ 5.5.13955077.1 None 920.2.a.j \(0\) \(0\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{3}-\beta _{4})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
9200.2.a.cv 9200.a 1.a $5$ $73.462$ 5.5.521397.1 None 4600.2.a.bd \(0\) \(0\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
9200.2.a.cw 9200.a 1.a $5$ $73.462$ 5.5.791953.1 None 4600.2.a.bc \(0\) \(3\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
9200.2.a.cx 9200.a 1.a $6$ $73.462$ 6.6.143376304.1 None 460.2.c.a \(0\) \(-4\) \(0\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9200.2.a.cy 9200.a 1.a $6$ $73.462$ 6.6.143376304.1 None 460.2.c.a \(0\) \(4\) \(0\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(2-\beta _{3})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
9200.2.a.cz 9200.a 1.a $7$ $73.462$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 920.2.e.b \(0\) \(-3\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.da 9200.a 1.a $7$ $73.462$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 575.2.a.k \(0\) \(0\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.db 9200.a 1.a $7$ $73.462$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 575.2.a.k \(0\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-\beta _{2}q^{7}+(1+\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.dc 9200.a 1.a $7$ $73.462$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 920.2.e.b \(0\) \(3\) \(0\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\beta _{6})q^{9}+\cdots\)
9200.2.a.dd 9200.a 1.a $8$ $73.462$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 920.2.e.c \(0\) \(-3\) \(0\) \(-7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
9200.2.a.de 9200.a 1.a $8$ $73.462$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 920.2.e.c \(0\) \(3\) \(0\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9200)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\)\(^{\oplus 2}\)