Properties

Label 5760.2.a
Level $5760$
Weight $2$
Character orbit 5760.a
Rep. character $\chi_{5760}(1,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $64$
Sturm bound $2304$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5760.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 64 \)
Sturm bound: \(2304\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5760))\).

Total New Old
Modular forms 1216 80 1136
Cusp forms 1089 80 1009
Eisenstein series 127 0 127

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

\(2\)\(3\)\(5\)FrickeDim
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(-\)\(+\)$-$\(12\)
\(+\)\(-\)\(-\)$+$\(10\)
\(-\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(12\)
\(-\)\(-\)\(-\)$-$\(14\)
Plus space\(+\)\(34\)
Minus space\(-\)\(46\)

Trace form

\( 80 q + O(q^{10}) \) \( 80 q + 80 q^{25} - 32 q^{41} + 144 q^{49} + 64 q^{73} - 32 q^{89} + 64 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5760))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
5760.2.a.a 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-6q^{11}-4q^{13}-4q^{17}+\cdots\)
5760.2.a.b 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+2q^{11}+8q^{23}+q^{25}+\cdots\)
5760.2.a.c 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-6q^{11}+2q^{13}+2q^{17}+\cdots\)
5760.2.a.d 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-2q^{13}+4q^{19}+q^{25}+\cdots\)
5760.2.a.e 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{13}-4q^{19}+q^{25}+\cdots\)
5760.2.a.f 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}-6q^{13}+6q^{17}+\cdots\)
5760.2.a.g 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
5760.2.a.h 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
5760.2.a.i 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}-4q^{13}-6q^{17}+6q^{19}+\cdots\)
5760.2.a.j 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}+4q^{13}+6q^{17}-6q^{19}+\cdots\)
5760.2.a.k 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}-2q^{13}-6q^{17}+6q^{19}+\cdots\)
5760.2.a.l 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}+4q^{13}+q^{25}-2q^{29}+\cdots\)
5760.2.a.m 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{11}-2q^{13}-6q^{17}-6q^{19}+\cdots\)
5760.2.a.n 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{11}+4q^{13}+q^{25}-2q^{29}+\cdots\)
5760.2.a.o 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}-4q^{13}-6q^{17}-6q^{19}+\cdots\)
5760.2.a.p 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{11}+4q^{13}+6q^{17}+6q^{19}+\cdots\)
5760.2.a.q 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
5760.2.a.r 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}-6q^{13}+6q^{17}+\cdots\)
5760.2.a.s 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
5760.2.a.t 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{13}-4q^{19}+q^{25}+\cdots\)
5760.2.a.u 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+2q^{13}+4q^{19}+q^{25}+\cdots\)
5760.2.a.v 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}+6q^{11}+2q^{13}+2q^{17}+\cdots\)
5760.2.a.w 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-2q^{11}-8q^{23}+q^{25}+\cdots\)
5760.2.a.x 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+6q^{11}-4q^{13}-4q^{17}+\cdots\)
5760.2.a.y 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-2q^{11}+8q^{23}+q^{25}+\cdots\)
5760.2.a.z 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}+6q^{11}+4q^{13}-4q^{17}+\cdots\)
5760.2.a.ba 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
5760.2.a.bb 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
5760.2.a.bc 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}+6q^{13}+6q^{17}+\cdots\)
5760.2.a.bd 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{13}+4q^{19}+q^{25}+\cdots\)
5760.2.a.be 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+2q^{13}-4q^{19}+q^{25}+\cdots\)
5760.2.a.bf 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+6q^{11}-2q^{13}+2q^{17}+\cdots\)
5760.2.a.bg 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}-4q^{13}+6q^{17}-6q^{19}+\cdots\)
5760.2.a.bh 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+4q^{13}-6q^{17}+6q^{19}+\cdots\)
5760.2.a.bi 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{11}-4q^{13}+q^{25}+2q^{29}+\cdots\)
5760.2.a.bj 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{11}+2q^{13}-6q^{17}+6q^{19}+\cdots\)
5760.2.a.bk 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}-4q^{13}+q^{25}+2q^{29}+\cdots\)
5760.2.a.bl 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}+2q^{13}-6q^{17}-6q^{19}+\cdots\)
5760.2.a.bm 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}-4q^{13}+6q^{17}+6q^{19}+\cdots\)
5760.2.a.bn 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+4q^{13}-6q^{17}-6q^{19}+\cdots\)
5760.2.a.bo 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-6q^{11}-2q^{13}+2q^{17}+\cdots\)
5760.2.a.bp 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-2q^{13}-4q^{19}+q^{25}+\cdots\)
5760.2.a.bq 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{13}+4q^{19}+q^{25}+\cdots\)
5760.2.a.br 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
5760.2.a.bs 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}+6q^{13}+6q^{17}+\cdots\)
5760.2.a.bt 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
5760.2.a.bu 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-6q^{11}+4q^{13}-4q^{17}+\cdots\)
5760.2.a.bv 5760.a 1.a $1$ $45.994$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+2q^{11}-8q^{23}+q^{25}+\cdots\)
5760.2.a.bw 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}-2q^{11}+2\beta q^{13}+\cdots\)
5760.2.a.bx 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+2q^{11}+(1+\beta )q^{13}+\cdots\)
5760.2.a.by 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+4q^{11}+(-3+\cdots)q^{13}+\cdots\)
5760.2.a.bz 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(-1-\beta )q^{7}+4q^{11}+(3-\beta )q^{13}+\cdots\)
5760.2.a.ca 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}-4q^{11}+(-3+\beta )q^{13}+\cdots\)
5760.2.a.cb 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}-4q^{11}+(3-\beta )q^{13}+\cdots\)
5760.2.a.cc 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}-2q^{11}+(1+\beta )q^{13}+\cdots\)
5760.2.a.cd 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+(1+\beta )q^{7}+2q^{11}+2\beta q^{13}+\cdots\)
5760.2.a.ce 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}-4q^{11}+(-3+\cdots)q^{13}+\cdots\)
5760.2.a.cf 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}-4q^{11}+(3-\beta )q^{13}+\cdots\)
5760.2.a.cg 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
5760.2.a.ch 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(-1-\beta )q^{7}+2q^{11}-2\beta q^{13}+\cdots\)
5760.2.a.ci 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}-2q^{11}-2\beta q^{13}+\cdots\)
5760.2.a.cj 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+2q^{11}+(-1-\beta )q^{13}+\cdots\)
5760.2.a.ck 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+4q^{11}+(-3+\beta )q^{13}+\cdots\)
5760.2.a.cl 5760.a 1.a $2$ $45.994$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+(1+\beta )q^{7}+4q^{11}+(3-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(640))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(960))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2880))\)\(^{\oplus 2}\)