Properties

Label 6240.2.a
Level $6240$
Weight $2$
Character orbit 6240.a
Rep. character $\chi_{6240}(1,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $58$
Sturm bound $2688$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6240.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 58 \)
Sturm bound: \(2688\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6240))\).

Total New Old
Modular forms 1376 96 1280
Cusp forms 1313 96 1217
Eisenstein series 63 0 63

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

\(2\)\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(40\)
Minus space\(-\)\(56\)

Trace form

\( 96 q + 96 q^{9} + O(q^{10}) \) \( 96 q + 96 q^{9} + 96 q^{25} + 96 q^{49} + 32 q^{53} + 32 q^{61} + 32 q^{77} + 96 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6240))\) 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 13
6240.2.a.a 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.b 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.c 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.d 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-q^{13}+q^{15}+2q^{17}+\cdots\)
6240.2.a.e 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots\)
6240.2.a.f 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.g 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.h 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(-1\) \(5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
6240.2.a.i 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
6240.2.a.j 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.k 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-q^{7}+q^{9}+3q^{11}-q^{13}+\cdots\)
6240.2.a.l 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.m 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
6240.2.a.n 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
6240.2.a.o 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}-3q^{11}+q^{13}+\cdots\)
6240.2.a.p 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}-q^{15}+\cdots\)
6240.2.a.q 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-5\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-5q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
6240.2.a.r 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.s 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.t 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.u 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
6240.2.a.v 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}-q^{15}+\cdots\)
6240.2.a.w 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
6240.2.a.x 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(-1\) \(4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.y 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
6240.2.a.z 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}+3q^{11}+q^{13}+\cdots\)
6240.2.a.ba 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
6240.2.a.bb 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-q^{13}+\cdots\)
6240.2.a.bc 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
6240.2.a.bd 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.be 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
6240.2.a.bf 6240.a 1.a $1$ $49.827$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
6240.2.a.bg 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(-2\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
6240.2.a.bh 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bi 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bj 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(4-\beta )q^{11}+\cdots\)
6240.2.a.bk 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(-2\) \(-2\) \(3\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6240.2.a.bl 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(-6\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-3-\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.bm 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(2\) \(-1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(4+\beta )q^{11}+\cdots\)
6240.2.a.bn 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
6240.2.a.bo 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-2\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-1-\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
6240.2.a.bp 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(-2\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
6240.2.a.bq 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\cdots\)
6240.2.a.br 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
6240.2.a.bs 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-2\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta q^{7}+q^{9}+(2-\beta )q^{11}+\cdots\)
6240.2.a.bt 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
6240.2.a.bu 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(-4-\beta )q^{11}+\cdots\)
6240.2.a.bv 6240.a 1.a $2$ $49.827$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(3+\beta )q^{7}+q^{9}+(2-2\beta )q^{11}+\cdots\)
6240.2.a.bw 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(-3\) \(-3\) \(-5\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-2-\beta _{2})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
6240.2.a.bx 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(-3\) \(-3\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.by 6240.a 1.a $3$ $49.827$ 3.3.568.1 None \(0\) \(-3\) \(3\) \(-5\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-2-\beta _{2})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.bz 6240.a 1.a $3$ $49.827$ 3.3.1849.1 None \(0\) \(-3\) \(3\) \(5\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(2-\beta _{1})q^{7}+q^{9}+(2-\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.ca 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(3\) \(-3\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+(1+\beta _{1}+\cdots)q^{11}+\cdots\)
6240.2.a.cb 6240.a 1.a $3$ $49.827$ 3.3.229.1 None \(0\) \(3\) \(-3\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(2+\beta _{2})q^{7}+q^{9}+\beta _{1}q^{11}+\cdots\)
6240.2.a.cc 6240.a 1.a $3$ $49.827$ 3.3.1849.1 None \(0\) \(3\) \(3\) \(-5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-2+\beta _{1})q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
6240.2.a.cd 6240.a 1.a $3$ $49.827$ 3.3.568.1 None \(0\) \(3\) \(3\) \(5\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(2+\beta _{2})q^{7}+q^{9}+(2-\beta _{2})q^{11}+\cdots\)
6240.2.a.ce 6240.a 1.a $4$ $49.827$ 4.4.15317.1 None \(0\) \(-4\) \(4\) \(-3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1-\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
6240.2.a.cf 6240.a 1.a $4$ $49.827$ 4.4.15317.1 None \(0\) \(4\) \(4\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1-\beta _{3})q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6240))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6240)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(130))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(260))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(390))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(520))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(780))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1040))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2080))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3120))\)\(^{\oplus 2}\)