Properties

Label 9920.2.a
Level $9920$
Weight $2$
Character orbit 9920.a
Rep. character $\chi_{9920}(1,\cdot)$
Character field $\Q$
Dimension $240$
Newform subspaces $80$
Sturm bound $3072$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 9920 = 2^{6} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9920.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 80 \)
Sturm bound: \(3072\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9920))\).

Total New Old
Modular forms 1560 240 1320
Cusp forms 1513 240 1273
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.

\(2\)\(5\)\(31\)FrickeDim
\(+\)\(+\)\(+\)$+$\(28\)
\(+\)\(+\)\(-\)$-$\(34\)
\(+\)\(-\)\(+\)$-$\(32\)
\(+\)\(-\)\(-\)$+$\(26\)
\(-\)\(+\)\(+\)$-$\(32\)
\(-\)\(+\)\(-\)$+$\(26\)
\(-\)\(-\)\(+\)$+$\(28\)
\(-\)\(-\)\(-\)$-$\(34\)
Plus space\(+\)\(108\)
Minus space\(-\)\(132\)

Trace form

\( 240 q + 240 q^{9} + O(q^{10}) \) \( 240 q + 240 q^{9} + 240 q^{25} + 32 q^{29} + 32 q^{33} + 32 q^{37} + 32 q^{41} + 240 q^{49} + 32 q^{53} + 32 q^{57} + 32 q^{77} + 304 q^{81} + 32 q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9920))\) 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 31
9920.2.a.a 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.a \(0\) \(-3\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+2q^{7}+6q^{9}+2q^{11}+\cdots\)
9920.2.a.b 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.g \(0\) \(-3\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+2q^{7}+6q^{9}+2q^{11}+\cdots\)
9920.2.a.c 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.e \(0\) \(-2\) \(1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
9920.2.a.d 9920.a 1.a $1$ $79.212$ \(\Q\) None 310.2.a.b \(0\) \(-2\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-2q^{11}-2q^{15}+\cdots\)
9920.2.a.e 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.f \(0\) \(-2\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-4q^{13}-2q^{15}+\cdots\)
9920.2.a.f 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.a \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}+6q^{11}+4q^{13}+\cdots\)
9920.2.a.g 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.b \(0\) \(-2\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
9920.2.a.h 9920.a 1.a $1$ $79.212$ \(\Q\) None 310.2.a.a \(0\) \(-2\) \(1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{13}+\cdots\)
9920.2.a.i 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.b \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}-2q^{9}-2q^{11}+\cdots\)
9920.2.a.j 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.a \(0\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}-2q^{9}+2q^{11}+\cdots\)
9920.2.a.k 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.c \(0\) \(-1\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}-2q^{9}-2q^{13}+\cdots\)
9920.2.a.l 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.c \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-4q^{11}+6q^{13}+\cdots\)
9920.2.a.m 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.a \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+2q^{13}-q^{15}+\cdots\)
9920.2.a.n 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.d \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{19}+\cdots\)
9920.2.a.o 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.b \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
9920.2.a.p 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.d \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
9920.2.a.q 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.d \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
9920.2.a.r 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.b \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
9920.2.a.s 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.d \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+4q^{11}-4q^{19}+\cdots\)
9920.2.a.t 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.b \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-3q^{9}+2q^{11}+6q^{13}+\cdots\)
9920.2.a.u 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.c \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-2q^{11}-2q^{13}+8q^{19}+\cdots\)
9920.2.a.v 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.c \(0\) \(0\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+2q^{11}-2q^{13}-8q^{19}+\cdots\)
9920.2.a.w 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.b \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}-2q^{11}+6q^{13}+\cdots\)
9920.2.a.x 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.a \(0\) \(1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}-2q^{11}+\cdots\)
9920.2.a.y 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.b \(0\) \(1\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}-2q^{9}+2q^{11}+\cdots\)
9920.2.a.z 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.a \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+2q^{13}+q^{15}+\cdots\)
9920.2.a.ba 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.c \(0\) \(1\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+4q^{11}+6q^{13}+\cdots\)
9920.2.a.bb 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.c \(0\) \(1\) \(1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}-2q^{9}-2q^{13}+\cdots\)
9920.2.a.bc 9920.a 1.a $1$ $79.212$ \(\Q\) None 310.2.a.a \(0\) \(2\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{13}+\cdots\)
9920.2.a.bd 9920.a 1.a $1$ $79.212$ \(\Q\) None 155.2.a.b \(0\) \(2\) \(1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
9920.2.a.be 9920.a 1.a $1$ $79.212$ \(\Q\) None 4960.2.a.a \(0\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-6q^{11}+4q^{13}+\cdots\)
9920.2.a.bf 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.f \(0\) \(2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-4q^{13}+2q^{15}+\cdots\)
9920.2.a.bg 9920.a 1.a $1$ $79.212$ \(\Q\) None 310.2.a.b \(0\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}+2q^{11}+2q^{15}+\cdots\)
9920.2.a.bh 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.e \(0\) \(2\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
9920.2.a.bi 9920.a 1.a $1$ $79.212$ \(\Q\) None 620.2.a.a \(0\) \(3\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}-2q^{7}+6q^{9}-2q^{11}+\cdots\)
9920.2.a.bj 9920.a 1.a $1$ $79.212$ \(\Q\) None 1240.2.a.g \(0\) \(3\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}-2q^{7}+6q^{9}-2q^{11}+\cdots\)
9920.2.a.bk 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{5}) \) None 4960.2.a.g \(0\) \(-2\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-q^{5}+(3+2\beta )q^{9}-2\beta q^{11}+\cdots\)
9920.2.a.bl 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1-2\beta )q^{9}+\cdots\)
9920.2.a.bm 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{17}) \) None 1240.2.a.h \(0\) \(-1\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(1+\beta )q^{9}+(-2+2\beta )q^{11}+\cdots\)
9920.2.a.bn 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{2}) \) None 1240.2.a.i \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-2q^{7}-q^{9}+(2+\beta )q^{11}+\cdots\)
9920.2.a.bo 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(0\) \(0\) \(-2\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-2q^{7}+3q^{9}+(-2+\beta )q^{11}+\cdots\)
9920.2.a.bp 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{2}) \) None 1240.2.a.i \(0\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+2q^{7}-q^{9}+(-2+\beta )q^{11}+\cdots\)
9920.2.a.bq 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(0\) \(0\) \(-2\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+2q^{7}+3q^{9}+(2+\beta )q^{11}+\cdots\)
9920.2.a.br 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{17}) \) None 1240.2.a.h \(0\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(1+\beta )q^{9}+(2-2\beta )q^{11}+\cdots\)
9920.2.a.bs 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{5}) \) None 4960.2.a.g \(0\) \(2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(3+2\beta )q^{9}+2\beta q^{11}+\cdots\)
9920.2.a.bt 9920.a 1.a $2$ $79.212$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(0\) \(2\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+2\beta q^{7}+(1+2\beta )q^{9}+\cdots\)
9920.2.a.bu 9920.a 1.a $3$ $79.212$ 3.3.148.1 None 1240.2.a.j \(0\) \(-3\) \(-3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(1-\beta _{1}-\beta _{2})q^{7}+\cdots\)
9920.2.a.bv 9920.a 1.a $3$ $79.212$ 3.3.756.1 None 620.2.a.d \(0\) \(-3\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}-\beta _{2}q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.bw 9920.a 1.a $3$ $79.212$ 3.3.148.1 None 310.2.a.e \(0\) \(-2\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
9920.2.a.bx 9920.a 1.a $3$ $79.212$ 3.3.148.1 None 310.2.a.e \(0\) \(2\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
9920.2.a.by 9920.a 1.a $3$ $79.212$ 3.3.148.1 None 1240.2.a.j \(0\) \(3\) \(-3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
9920.2.a.bz 9920.a 1.a $3$ $79.212$ 3.3.756.1 None 620.2.a.d \(0\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+\beta _{2}q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.ca 9920.a 1.a $4$ $79.212$ 4.4.25492.1 None 620.2.a.e \(0\) \(-3\) \(-4\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{2}-\beta _{3})q^{7}+\cdots\)
9920.2.a.cb 9920.a 1.a $4$ $79.212$ 4.4.8468.1 None 155.2.a.e \(0\) \(-1\) \(-4\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{1}+2\beta _{2}-\beta _{3})q^{7}+\cdots\)
9920.2.a.cc 9920.a 1.a $4$ $79.212$ 4.4.112820.1 None 1240.2.a.k \(0\) \(-1\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{1}-\beta _{3})q^{7}+\cdots\)
9920.2.a.cd 9920.a 1.a $4$ $79.212$ 4.4.20308.1 None 155.2.a.d \(0\) \(-1\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
9920.2.a.ce 9920.a 1.a $4$ $79.212$ 4.4.6224.1 None 4960.2.a.i \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{2})q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
9920.2.a.cf 9920.a 1.a $4$ $79.212$ 4.4.6224.1 None 4960.2.a.i \(0\) \(0\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-\beta _{1}-\beta _{2})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.cg 9920.a 1.a $4$ $79.212$ 4.4.8468.1 None 155.2.a.e \(0\) \(1\) \(-4\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
9920.2.a.ch 9920.a 1.a $4$ $79.212$ 4.4.20308.1 None 155.2.a.d \(0\) \(1\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{3}+q^{5}+\beta _{2}q^{7}+(2-\beta _{1}-2\beta _{2}+\cdots)q^{9}+\cdots\)
9920.2.a.ci 9920.a 1.a $4$ $79.212$ 4.4.112820.1 None 1240.2.a.k \(0\) \(1\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1-\beta _{1}+\beta _{3})q^{7}+(2+\cdots)q^{9}+\cdots\)
9920.2.a.cj 9920.a 1.a $4$ $79.212$ 4.4.25492.1 None 620.2.a.e \(0\) \(3\) \(-4\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-2+\beta _{2}+\beta _{3})q^{7}+\cdots\)
9920.2.a.ck 9920.a 1.a $6$ $79.212$ 6.6.50574608.1 None 4960.2.a.l \(0\) \(-4\) \(6\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{5})q^{7}+\cdots\)
9920.2.a.cl 9920.a 1.a $6$ $79.212$ 6.6.197463312.1 None 4960.2.a.k \(0\) \(-4\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}-\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.cm 9920.a 1.a $6$ $79.212$ 6.6.473125168.1 None 1240.2.a.l \(0\) \(-3\) \(6\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-\beta _{2}-\beta _{4})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.cn 9920.a 1.a $6$ $79.212$ 6.6.27554944.1 None 4960.2.a.m \(0\) \(-2\) \(-6\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1-\beta _{4})q^{7}+(-1+\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.co 9920.a 1.a $6$ $79.212$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1240.2.a.m \(0\) \(-1\) \(-6\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+\beta _{2}q^{7}+(4-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
9920.2.a.cp 9920.a 1.a $6$ $79.212$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 1240.2.a.m \(0\) \(1\) \(-6\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(4-\beta _{3}+\beta _{4}+\cdots)q^{9}+\cdots\)
9920.2.a.cq 9920.a 1.a $6$ $79.212$ 6.6.27554944.1 None 4960.2.a.m \(0\) \(2\) \(-6\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1+\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots\)
9920.2.a.cr 9920.a 1.a $6$ $79.212$ 6.6.473125168.1 None 1240.2.a.l \(0\) \(3\) \(6\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{2}+\beta _{4})q^{7}+(\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
9920.2.a.cs 9920.a 1.a $6$ $79.212$ 6.6.197463312.1 None 4960.2.a.k \(0\) \(4\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+\beta _{4}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.ct 9920.a 1.a $6$ $79.212$ 6.6.50574608.1 None 4960.2.a.l \(0\) \(4\) \(6\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots\)
9920.2.a.cu 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.q \(0\) \(-4\) \(-8\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+\beta _{7}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.cv 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.r \(0\) \(-2\) \(8\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+q^{5}+(-1+\beta _{2})q^{7}+(1-\beta _{5}+\cdots)q^{9}+\cdots\)
9920.2.a.cw 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.s \(0\) \(0\) \(8\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+q^{5}+(-1-\beta _{5})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9920.2.a.cx 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.s \(0\) \(0\) \(8\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+q^{5}+(1+\beta _{5})q^{7}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
9920.2.a.cy 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.r \(0\) \(2\) \(8\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1-\beta _{5}+\cdots)q^{9}+\cdots\)
9920.2.a.cz 9920.a 1.a $8$ $79.212$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 4960.2.a.q \(0\) \(4\) \(-8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}-\beta _{7}q^{7}+(2-\beta _{1}+\cdots)q^{9}+\cdots\)
9920.2.a.da 9920.a 1.a $9$ $79.212$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 4960.2.a.w \(0\) \(0\) \(-9\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(1-\beta _{4}+\beta _{5}+\cdots)q^{9}+\cdots\)
9920.2.a.db 9920.a 1.a $9$ $79.212$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 4960.2.a.w \(0\) \(0\) \(-9\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}-\beta _{3}q^{7}+(1-\beta _{4}+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9920))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(9920)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(248))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(310))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(496))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(620))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(992))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1984))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2480))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4960))\)\(^{\oplus 2}\)