Properties

Label 6960.2.a
Level $6960$
Weight $2$
Character orbit 6960.a
Rep. character $\chi_{6960}(1,\cdot)$
Character field $\Q$
Dimension $112$
Newform subspaces $69$
Sturm bound $2880$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6960 = 2^{4} \cdot 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6960.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 69 \)
Sturm bound: \(2880\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6960))\).

Total New Old
Modular forms 1464 112 1352
Cusp forms 1417 112 1305
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.

\(2\)\(3\)\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(10\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(50\)
Minus space\(-\)\(62\)

Trace form

\( 112 q + 4 q^{3} + 8 q^{7} + 112 q^{9} + O(q^{10}) \) \( 112 q + 4 q^{3} + 8 q^{7} + 112 q^{9} - 4 q^{15} + 112 q^{25} + 4 q^{27} + 8 q^{39} - 16 q^{41} + 32 q^{43} + 48 q^{47} + 112 q^{49} - 8 q^{51} - 16 q^{55} + 16 q^{57} + 16 q^{59} + 16 q^{61} + 8 q^{63} - 16 q^{65} + 8 q^{67} + 16 q^{69} - 32 q^{71} + 16 q^{73} + 4 q^{75} + 48 q^{79} + 112 q^{81} + 16 q^{85} - 12 q^{87} - 16 q^{89} - 40 q^{91} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6960))\) 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 29
6960.2.a.a 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.o \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6960.2.a.b 6960.a 1.a $1$ $55.576$ \(\Q\) None 435.2.a.c \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
6960.2.a.c 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.n \(0\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
6960.2.a.d 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.b \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
6960.2.a.e 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.m \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}+q^{9}+3q^{11}+3q^{13}+\cdots\)
6960.2.a.f 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.e \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6960.2.a.g 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.l \(0\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots\)
6960.2.a.h 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.k \(0\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-3q^{11}-6q^{13}+\cdots\)
6960.2.a.i 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.i \(0\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
6960.2.a.j 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.j \(0\) \(-1\) \(-1\) \(2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}+4q^{13}+\cdots\)
6960.2.a.k 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.t \(0\) \(-1\) \(1\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
6960.2.a.l 6960.a 1.a $1$ $55.576$ \(\Q\) None 435.2.a.d \(0\) \(-1\) \(1\) \(-4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
6960.2.a.m 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.h \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6960.2.a.n 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.i \(0\) \(-1\) \(1\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}-4q^{13}+\cdots\)
6960.2.a.o 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.s \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
6960.2.a.p 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.d \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}+6q^{17}+\cdots\)
6960.2.a.q 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.r \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
6960.2.a.r 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.h \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
6960.2.a.s 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.q \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{11}-2q^{13}+\cdots\)
6960.2.a.t 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.p \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
6960.2.a.u 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.g \(0\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
6960.2.a.v 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.c \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
6960.2.a.w 6960.a 1.a $1$ $55.576$ \(\Q\) None 435.2.a.a \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+6q^{13}-q^{15}+\cdots\)
6960.2.a.x 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.f \(0\) \(-1\) \(1\) \(5\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}+q^{9}-5q^{11}-5q^{13}+\cdots\)
6960.2.a.y 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.c \(0\) \(1\) \(-1\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}-2q^{11}-q^{15}+\cdots\)
6960.2.a.z 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.a \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+6q^{11}+6q^{13}+\cdots\)
6960.2.a.ba 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.b \(0\) \(1\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)
6960.2.a.bb 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.a \(0\) \(1\) \(-1\) \(2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-6q^{11}+6q^{13}+\cdots\)
6960.2.a.bc 6960.a 1.a $1$ $55.576$ \(\Q\) None 435.2.a.b \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{11}+6q^{13}+\cdots\)
6960.2.a.bd 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.e \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
6960.2.a.be 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.g \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)
6960.2.a.bf 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.d \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}+3q^{13}+\cdots\)
6960.2.a.bg 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.h \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-6q^{11}+4q^{13}+\cdots\)
6960.2.a.bh 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.c \(0\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
6960.2.a.bi 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.g \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots\)
6960.2.a.bj 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.a \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-6q^{13}+q^{15}-2q^{17}+\cdots\)
6960.2.a.bk 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.f \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-4q^{13}+q^{15}-2q^{17}+\cdots\)
6960.2.a.bl 6960.a 1.a $1$ $55.576$ \(\Q\) None 1740.2.a.b \(0\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-3q^{11}-2q^{13}+\cdots\)
6960.2.a.bm 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.e \(0\) \(1\) \(1\) \(3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6960.2.a.bn 6960.a 1.a $1$ $55.576$ \(\Q\) None 3480.2.a.d \(0\) \(1\) \(1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
6960.2.a.bo 6960.a 1.a $1$ $55.576$ \(\Q\) None 870.2.a.f \(0\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
6960.2.a.bp 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{5}) \) None 435.2.a.g \(0\) \(-2\) \(-2\) \(-4\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
6960.2.a.bq 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{5}) \) None 870.2.a.m \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
6960.2.a.br 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 1740.2.a.m \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6960.2.a.bs 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{33}) \) None 1740.2.a.l \(0\) \(-2\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6960.2.a.bt 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 3480.2.a.x \(0\) \(-2\) \(-2\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(3-\beta )q^{11}+\cdots\)
6960.2.a.bu 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{5}) \) None 435.2.a.e \(0\) \(-2\) \(-2\) \(6\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}+(1+2\beta )q^{11}+\cdots\)
6960.2.a.bv 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{57}) \) None 1740.2.a.n \(0\) \(-2\) \(2\) \(-4\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6960.2.a.bw 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{21}) \) None 435.2.a.f \(0\) \(-2\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-5q^{11}+\beta q^{13}+\cdots\)
6960.2.a.bx 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 435.2.a.h \(0\) \(-2\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
6960.2.a.by 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 3480.2.a.z \(0\) \(-2\) \(2\) \(-1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6960.2.a.bz 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{33}) \) None 3480.2.a.y \(0\) \(-2\) \(2\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
6960.2.a.ca 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{33}) \) None 3480.2.a.v \(0\) \(2\) \(-2\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
6960.2.a.cb 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 1740.2.a.j \(0\) \(2\) \(-2\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6960.2.a.cc 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{2}) \) None 870.2.a.l \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
6960.2.a.cd 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{33}) \) None 1740.2.a.i \(0\) \(2\) \(-2\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
6960.2.a.ce 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{13}) \) None 870.2.a.j \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
6960.2.a.cf 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 3480.2.a.u \(0\) \(2\) \(-2\) \(5\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(3-\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
6960.2.a.cg 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{2}) \) None 870.2.a.k \(0\) \(2\) \(2\) \(-4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-2+\beta )q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)
6960.2.a.ch 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 3480.2.a.w \(0\) \(2\) \(2\) \(-3\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6960.2.a.ci 6960.a 1.a $2$ $55.576$ \(\Q(\sqrt{17}) \) None 1740.2.a.k \(0\) \(2\) \(2\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(3-\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
6960.2.a.cj 6960.a 1.a $3$ $55.576$ 3.3.229.1 None 3480.2.a.ba \(0\) \(3\) \(-3\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+\beta _{2}q^{11}+\cdots\)
6960.2.a.ck 6960.a 1.a $3$ $55.576$ 3.3.229.1 None 3480.2.a.bb \(0\) \(3\) \(3\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6960.2.a.cl 6960.a 1.a $3$ $55.576$ 3.3.469.1 None 435.2.a.i \(0\) \(3\) \(3\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+\beta _{2})q^{7}+q^{9}-3q^{11}+\cdots\)
6960.2.a.cm 6960.a 1.a $4$ $55.576$ 4.4.58397.1 None 3480.2.a.bc \(0\) \(-4\) \(-4\) \(3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta _{3})q^{7}+q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
6960.2.a.cn 6960.a 1.a $4$ $55.576$ 4.4.69272.1 None 3480.2.a.bd \(0\) \(-4\) \(4\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{3}q^{11}+\cdots\)
6960.2.a.co 6960.a 1.a $4$ $55.576$ 4.4.2225.1 None 435.2.a.j \(0\) \(4\) \(-4\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6960.2.a.cp 6960.a 1.a $5$ $55.576$ 5.5.18396776.1 None 3480.2.a.be \(0\) \(5\) \(-5\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta _{2}q^{7}+q^{9}+(1-\beta _{3}+\cdots)q^{11}+\cdots\)
6960.2.a.cq 6960.a 1.a $5$ $55.576$ 5.5.1025428.1 None 3480.2.a.bf \(0\) \(5\) \(5\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6960)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(232))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(290))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(435))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(580))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(696))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(870))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1740))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3480))\)\(^{\oplus 2}\)