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Properties

Label 9150.2.a
Level $9150$
Weight $2$
Character orbit 9150.a
Rep. character $\chi_{9150}(1,\cdot)$
Character field $\Q$
Dimension $190$
Newform subspaces $63$
Sturm bound $3720$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 9150 = 2 \cdot 3 \cdot 5^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 63 \)
Sturm bound: \(3720\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9150))\).

Total New Old
Modular forms 1884 190 1694
Cusp forms 1837 190 1647
Eisenstein series 47 0 47

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

\(2\)\(3\)\(5\)\(61\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(10\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(13\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(13\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(15\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(9\)
Plus space\(+\)\(86\)
Minus space\(-\)\(104\)

Trace form

\( 190 q + 190 q^{4} - 2 q^{6} - 4 q^{7} + 190 q^{9} + O(q^{10}) \) \( 190 q + 190 q^{4} - 2 q^{6} - 4 q^{7} + 190 q^{9} - 8 q^{14} + 190 q^{16} + 16 q^{17} - 8 q^{19} - 4 q^{21} - 12 q^{22} - 2 q^{24} - 8 q^{26} - 4 q^{28} - 24 q^{29} - 20 q^{31} - 8 q^{33} + 190 q^{36} - 12 q^{37} + 8 q^{38} - 8 q^{39} - 32 q^{41} + 4 q^{42} - 20 q^{43} - 16 q^{46} - 8 q^{47} + 170 q^{49} - 4 q^{51} - 24 q^{53} - 2 q^{54} - 8 q^{56} - 8 q^{57} + 4 q^{58} - 32 q^{59} - 6 q^{61} - 4 q^{62} - 4 q^{63} + 190 q^{64} - 8 q^{66} + 12 q^{67} + 16 q^{68} - 8 q^{71} - 20 q^{73} - 8 q^{74} - 8 q^{76} - 12 q^{77} - 12 q^{78} + 20 q^{79} + 190 q^{81} + 24 q^{82} + 8 q^{83} - 4 q^{84} - 4 q^{86} + 4 q^{87} - 12 q^{88} - 48 q^{89} - 64 q^{91} - 4 q^{93} - 48 q^{94} - 2 q^{96} + 40 q^{97} - 16 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9150))\) 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 3 5 61
9150.2.a.a 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.k \(-1\) \(-1\) \(0\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-5q^{7}-q^{8}+\cdots\)
9150.2.a.b 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.b \(-1\) \(-1\) \(0\) \(-3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\)
9150.2.a.c 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.c \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
9150.2.a.d 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.g \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
9150.2.a.e 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.f \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
9150.2.a.f 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.l \(-1\) \(-1\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
9150.2.a.g 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.j \(-1\) \(-1\) \(0\) \(4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+4q^{7}-q^{8}+\cdots\)
9150.2.a.h 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.i \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
9150.2.a.i 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.e \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
9150.2.a.j 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.f \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
9150.2.a.k 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.g \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
9150.2.a.l 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.a \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
9150.2.a.m 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.h \(-1\) \(1\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
9150.2.a.n 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.d \(-1\) \(1\) \(0\) \(3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+3q^{7}-q^{8}+\cdots\)
9150.2.a.o 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.d \(-1\) \(1\) \(0\) \(4\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\)
9150.2.a.p 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.d \(1\) \(-1\) \(0\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\)
9150.2.a.q 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.c \(1\) \(-1\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\)
9150.2.a.r 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.a \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
9150.2.a.s 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.b \(1\) \(-1\) \(0\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\)
9150.2.a.t 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.d \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
9150.2.a.u 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.e \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
9150.2.a.v 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.c \(1\) \(-1\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\)
9150.2.a.w 9150.a 1.a $1$ $73.063$ \(\Q\) None 366.2.a.a \(1\) \(1\) \(0\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-4q^{7}+q^{8}+\cdots\)
9150.2.a.x 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.b \(1\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
9150.2.a.y 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.c \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
9150.2.a.z 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.a.a \(1\) \(1\) \(0\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
9150.2.a.ba 9150.a 1.a $1$ $73.063$ \(\Q\) None 1830.2.d.b \(1\) \(1\) \(0\) \(3\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\)
9150.2.a.bb 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{17}) \) None 1830.2.a.r \(-2\) \(-2\) \(0\) \(-5\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-\beta )q^{7}+\cdots\)
9150.2.a.bc 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{2}) \) None 1830.2.a.q \(-2\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta q^{7}-q^{8}+\cdots\)
9150.2.a.bd 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{65}) \) None 1830.2.a.o \(-2\) \(2\) \(0\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-\beta q^{7}-q^{8}+\cdots\)
9150.2.a.be 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{6}) \) None 1830.2.a.n \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\)
9150.2.a.bf 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{2}) \) None 1830.2.a.p \(-2\) \(2\) \(0\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(2+\beta )q^{7}+\cdots\)
9150.2.a.bg 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{17}) \) None 1830.2.a.m \(2\) \(2\) \(0\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
9150.2.a.bh 9150.a 1.a $2$ $73.063$ \(\Q(\sqrt{17}) \) None 366.2.a.h \(2\) \(2\) \(0\) \(3\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta )q^{7}+\cdots\)
9150.2.a.bi 9150.a 1.a $3$ $73.063$ 3.3.148.1 None 1830.2.d.e \(-3\) \(-3\) \(0\) \(4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(1+\beta _{1})q^{7}+\cdots\)
9150.2.a.bj 9150.a 1.a $3$ $73.063$ 3.3.1708.1 None 1830.2.a.u \(3\) \(-3\) \(0\) \(-5\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
9150.2.a.bk 9150.a 1.a $3$ $73.063$ 3.3.316.1 None 1830.2.a.s \(3\) \(3\) \(0\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
9150.2.a.bl 9150.a 1.a $3$ $73.063$ 3.3.148.1 None 1830.2.d.e \(3\) \(3\) \(0\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
9150.2.a.bm 9150.a 1.a $3$ $73.063$ 3.3.316.1 None 1830.2.a.t \(3\) \(3\) \(0\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
9150.2.a.bn 9150.a 1.a $4$ $73.063$ 4.4.250528.1 None 1830.2.a.w \(-4\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta _{1}q^{7}-q^{8}+\cdots\)
9150.2.a.bo 9150.a 1.a $4$ $73.063$ 4.4.174508.1 None 1830.2.a.v \(4\) \(-4\) \(0\) \(-3\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-1+\beta _{3})q^{7}+\cdots\)
9150.2.a.bp 9150.a 1.a $5$ $73.063$ 5.5.3183073.1 None 9150.2.a.bp \(-5\) \(-5\) \(0\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-1-\beta _{3}+\cdots)q^{7}+\cdots\)
9150.2.a.bq 9150.a 1.a $5$ $73.063$ 5.5.249689.1 None 9150.2.a.bq \(-5\) \(-5\) \(0\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta _{4}q^{7}-q^{8}+\cdots\)
9150.2.a.br 9150.a 1.a $5$ $73.063$ 5.5.205225.1 None 9150.2.a.br \(-5\) \(-5\) \(0\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9150.2.a.bs 9150.a 1.a $5$ $73.063$ 5.5.726369.1 None 9150.2.a.bs \(-5\) \(-5\) \(0\) \(6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(1-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
9150.2.a.bt 9150.a 1.a $5$ $73.063$ 5.5.3435009.1 None 9150.2.a.bt \(-5\) \(5\) \(0\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
9150.2.a.bu 9150.a 1.a $5$ $73.063$ 5.5.624897.1 None 9150.2.a.bu \(-5\) \(5\) \(0\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9150.2.a.bv 9150.a 1.a $5$ $73.063$ 5.5.288633.1 None 9150.2.a.bv \(-5\) \(5\) \(0\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta _{3}q^{7}-q^{8}+\cdots\)
9150.2.a.bw 9150.a 1.a $5$ $73.063$ 5.5.1427281.1 None 9150.2.a.bw \(-5\) \(5\) \(0\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(\beta _{1}-\beta _{4})q^{7}+\cdots\)
9150.2.a.bx 9150.a 1.a $5$ $73.063$ 5.5.1427281.1 None 9150.2.a.bw \(5\) \(-5\) \(0\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-\beta _{1}+\beta _{4})q^{7}+\cdots\)
9150.2.a.by 9150.a 1.a $5$ $73.063$ 5.5.288633.1 None 9150.2.a.bv \(5\) \(-5\) \(0\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-\beta _{3}q^{7}+q^{8}+\cdots\)
9150.2.a.bz 9150.a 1.a $5$ $73.063$ 5.5.624897.1 None 9150.2.a.bu \(5\) \(-5\) \(0\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
9150.2.a.ca 9150.a 1.a $5$ $73.063$ 5.5.3435009.1 None 9150.2.a.bt \(5\) \(-5\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
9150.2.a.cb 9150.a 1.a $5$ $73.063$ 5.5.726369.1 None 9150.2.a.bs \(5\) \(5\) \(0\) \(-6\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
9150.2.a.cc 9150.a 1.a $5$ $73.063$ 5.5.205225.1 None 9150.2.a.br \(5\) \(5\) \(0\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
9150.2.a.cd 9150.a 1.a $5$ $73.063$ 5.5.249689.1 None 9150.2.a.bq \(5\) \(5\) \(0\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta _{4}q^{7}+q^{8}+\cdots\)
9150.2.a.ce 9150.a 1.a $5$ $73.063$ 5.5.3183073.1 None 9150.2.a.bp \(5\) \(5\) \(0\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+(1+\beta _{3})q^{7}+\cdots\)
9150.2.a.cf 9150.a 1.a $6$ $73.063$ 6.6.556008944.1 None 1830.2.d.f \(-6\) \(6\) \(0\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta _{3}q^{7}-q^{8}+\cdots\)
9150.2.a.cg 9150.a 1.a $6$ $73.063$ 6.6.556008944.1 None 1830.2.d.f \(6\) \(-6\) \(0\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-\beta _{3}q^{7}+q^{8}+\cdots\)
9150.2.a.ch 9150.a 1.a $8$ $73.063$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1830.2.d.g \(-8\) \(8\) \(0\) \(-5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta _{5}+\cdots)q^{7}+\cdots\)
9150.2.a.ci 9150.a 1.a $8$ $73.063$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1830.2.d.g \(8\) \(-8\) \(0\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta _{5})q^{7}+\cdots\)
9150.2.a.cj 9150.a 1.a $9$ $73.063$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1830.2.d.h \(-9\) \(-9\) \(0\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+\beta _{8}q^{7}-q^{8}+\cdots\)
9150.2.a.ck 9150.a 1.a $9$ $73.063$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1830.2.d.h \(9\) \(9\) \(0\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-\beta _{8}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9150)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(305))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(366))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(610))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(915))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1830))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4575))\)\(^{\oplus 2}\)