Properties

Label 4928.2.a
Level $4928$
Weight $2$
Character orbit 4928.a
Rep. character $\chi_{4928}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $64$
Sturm bound $1536$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4928 = 2^{6} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4928.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 64 \)
Sturm bound: \(1536\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(13\), \(17\), \(19\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4928))\).

Total New Old
Modular forms 792 120 672
Cusp forms 745 120 625
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.

\(2\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(14\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(16\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(52\)
Minus space\(-\)\(68\)

Trace form

\( 120 q + 120 q^{9} + O(q^{10}) \) \( 120 q + 120 q^{9} + 16 q^{17} + 136 q^{25} + 16 q^{41} - 48 q^{45} + 120 q^{49} - 48 q^{53} + 64 q^{61} + 16 q^{69} - 16 q^{73} + 120 q^{81} + 64 q^{85} - 16 q^{89} + 48 q^{93} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4928))\) 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 7 11
4928.2.a.a 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-3\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots\)
4928.2.a.b 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(-4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4928.2.a.c 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
4928.2.a.d 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(-2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}+4q^{13}+\cdots\)
4928.2.a.e 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}+4q^{15}+\cdots\)
4928.2.a.f 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+q^{11}-6q^{17}+\cdots\)
4928.2.a.g 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
4928.2.a.h 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-2\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4928.2.a.i 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots\)
4928.2.a.j 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
4928.2.a.k 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}-2q^{9}+q^{11}-q^{15}+\cdots\)
4928.2.a.l 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}+q^{11}+4q^{13}+\cdots\)
4928.2.a.m 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(-1\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
4928.2.a.n 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots\)
4928.2.a.o 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
4928.2.a.p 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}-q^{11}+2q^{13}+4q^{17}+\cdots\)
4928.2.a.q 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}+q^{11}+6q^{13}+2q^{19}+\cdots\)
4928.2.a.r 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}-q^{11}+6q^{13}-2q^{19}+\cdots\)
4928.2.a.s 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+q^{11}+2q^{13}+4q^{17}+\cdots\)
4928.2.a.t 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
4928.2.a.u 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots\)
4928.2.a.v 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-3q^{9}+q^{11}-2q^{13}+\cdots\)
4928.2.a.w 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(0\) \(4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}-3q^{9}-q^{11}-2q^{13}+\cdots\)
4928.2.a.x 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(1\) \(-3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
4928.2.a.y 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
4928.2.a.z 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}-2q^{9}-q^{11}+4q^{13}+\cdots\)
4928.2.a.ba 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}-2q^{9}-q^{11}+q^{15}+\cdots\)
4928.2.a.bb 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(1\) \(3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-q^{7}-2q^{9}+q^{11}-6q^{13}+\cdots\)
4928.2.a.bc 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
4928.2.a.bd 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(-2\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}-q^{7}+q^{9}-q^{11}-4q^{15}+\cdots\)
4928.2.a.be 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4928.2.a.bf 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(-2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}+q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
4928.2.a.bg 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}-q^{11}-6q^{17}+\cdots\)
4928.2.a.bh 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}-q^{7}+q^{9}-q^{11}-4q^{13}+\cdots\)
4928.2.a.bi 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(2\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
4928.2.a.bj 4928.a 1.a $1$ $39.350$ \(\Q\) None \(0\) \(3\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
4928.2.a.bk 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots\)
4928.2.a.bl 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+q^{7}+(1-2\beta )q^{9}+\cdots\)
4928.2.a.bm 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(4\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+2q^{5}+q^{7}+(3+2\beta )q^{9}+\cdots\)
4928.2.a.bn 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-\beta q^{5}-q^{7}+(1+\beta )q^{9}-q^{11}+\cdots\)
4928.2.a.bo 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
4928.2.a.bp 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-4\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}-q^{7}+3q^{9}+q^{11}+\cdots\)
4928.2.a.bq 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-4\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+q^{7}+3q^{9}-q^{11}+\cdots\)
4928.2.a.br 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}+q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
4928.2.a.bs 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(3\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}-q^{7}+(1+\beta )q^{9}+\cdots\)
4928.2.a.bt 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
4928.2.a.bu 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2\beta q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
4928.2.a.bv 4928.a 1.a $2$ $39.350$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+2q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
4928.2.a.bw 4928.a 1.a $3$ $39.350$ 3.3.229.1 None \(0\) \(-1\) \(-1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{2}q^{5}+q^{7}+(1-\beta _{1})q^{9}+\cdots\)
4928.2.a.bx 4928.a 1.a $3$ $39.350$ 3.3.1016.1 None \(0\) \(-1\) \(1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4928.2.a.by 4928.a 1.a $3$ $39.350$ 3.3.316.1 None \(0\) \(-1\) \(3\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}-q^{7}+\beta _{2}q^{9}+\cdots\)
4928.2.a.bz 4928.a 1.a $3$ $39.350$ 3.3.229.1 None \(0\) \(1\) \(-1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+\beta _{2}q^{5}-q^{7}+(1-\beta _{1})q^{9}+\cdots\)
4928.2.a.ca 4928.a 1.a $3$ $39.350$ 3.3.1016.1 None \(0\) \(1\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4928.2.a.cb 4928.a 1.a $3$ $39.350$ 3.3.316.1 None \(0\) \(1\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{2})q^{5}+q^{7}+\beta _{2}q^{9}+\cdots\)
4928.2.a.cc 4928.a 1.a $4$ $39.350$ 4.4.11348.1 None \(0\) \(-1\) \(-5\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4928.2.a.cd 4928.a 1.a $4$ $39.350$ 4.4.2777.1 None \(0\) \(-1\) \(-5\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4928.2.a.ce 4928.a 1.a $4$ $39.350$ 4.4.10273.1 None \(0\) \(-1\) \(1\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{1}q^{5}-q^{7}+(2-\beta _{2})q^{9}+\cdots\)
4928.2.a.cf 4928.a 1.a $4$ $39.350$ 4.4.8468.1 None \(0\) \(-1\) \(5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{5}+q^{7}+\beta _{3}q^{9}+\cdots\)
4928.2.a.cg 4928.a 1.a $4$ $39.350$ 4.4.2777.1 None \(0\) \(1\) \(-5\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4928.2.a.ch 4928.a 1.a $4$ $39.350$ 4.4.11348.1 None \(0\) \(1\) \(-5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-1+\beta _{1})q^{5}+q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
4928.2.a.ci 4928.a 1.a $4$ $39.350$ 4.4.10273.1 None \(0\) \(1\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{2})q^{9}+\cdots\)
4928.2.a.cj 4928.a 1.a $4$ $39.350$ 4.4.8468.1 None \(0\) \(1\) \(5\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}-q^{7}+\beta _{3}q^{9}+\cdots\)
4928.2.a.ck 4928.a 1.a $5$ $39.350$ 5.5.2042356.1 None \(0\) \(-3\) \(1\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{3}-\beta _{3}q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
4928.2.a.cl 4928.a 1.a $5$ $39.350$ 5.5.2042356.1 None \(0\) \(3\) \(1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}-\beta _{3}q^{5}+q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4928))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4928)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2464))\)\(^{\oplus 2}\)