Properties

Label 7840.2.a
Level $7840$
Weight $2$
Character orbit 7840.a
Rep. character $\chi_{7840}(1,\cdot)$
Character field $\Q$
Dimension $164$
Newform subspaces $61$
Sturm bound $2688$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 7840 = 2^{5} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7840.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 61 \)
Sturm bound: \(2688\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7840))\).

Total New Old
Modular forms 1408 164 1244
Cusp forms 1281 164 1117
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.

\(2\)\(5\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(21\)
\(+\)\(+\)\(-\)$-$\(21\)
\(+\)\(-\)\(+\)$-$\(23\)
\(+\)\(-\)\(-\)$+$\(18\)
\(-\)\(+\)\(+\)$-$\(19\)
\(-\)\(+\)\(-\)$+$\(21\)
\(-\)\(-\)\(+\)$+$\(17\)
\(-\)\(-\)\(-\)$-$\(24\)
Plus space\(+\)\(77\)
Minus space\(-\)\(87\)

Trace form

\( 164 q + 172 q^{9} + O(q^{10}) \) \( 164 q + 172 q^{9} + 16 q^{13} + 8 q^{17} + 164 q^{25} - 8 q^{29} - 16 q^{33} + 16 q^{37} - 32 q^{41} - 8 q^{45} - 16 q^{53} - 8 q^{65} - 40 q^{69} + 40 q^{73} + 188 q^{81} + 40 q^{89} - 16 q^{93} + 56 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7840))\) 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 5 7
7840.2.a.a 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-3\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}+6q^{9}+3q^{11}-q^{13}+\cdots\)
7840.2.a.b 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-3\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+6q^{9}+q^{11}+q^{13}+\cdots\)
7840.2.a.c 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}+3q^{11}+q^{13}+\cdots\)
7840.2.a.d 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-3q^{11}-q^{13}+\cdots\)
7840.2.a.e 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
7840.2.a.f 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-3q^{11}+7q^{13}+\cdots\)
7840.2.a.g 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-2q^{11}+2q^{13}+\cdots\)
7840.2.a.h 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
7840.2.a.i 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-q^{11}-3q^{13}+\cdots\)
7840.2.a.j 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}-q^{11}+q^{13}-q^{15}+\cdots\)
7840.2.a.k 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{9}+2q^{11}-2q^{13}+\cdots\)
7840.2.a.l 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+2q^{13}-2q^{17}-8q^{19}+\cdots\)
7840.2.a.m 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+2q^{13}-2q^{17}+8q^{19}+\cdots\)
7840.2.a.n 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-4q^{11}-2q^{13}-6q^{17}+\cdots\)
7840.2.a.o 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+4q^{11}-2q^{13}-6q^{17}+\cdots\)
7840.2.a.p 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-5q^{11}-5q^{13}+\cdots\)
7840.2.a.q 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+2q^{11}+2q^{13}+\cdots\)
7840.2.a.r 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}+3q^{11}+7q^{13}+\cdots\)
7840.2.a.s 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}-2q^{11}-2q^{13}+\cdots\)
7840.2.a.t 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+q^{11}-3q^{13}+\cdots\)
7840.2.a.u 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{9}+q^{11}+q^{13}+q^{15}+\cdots\)
7840.2.a.v 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{9}-3q^{11}+q^{13}+\cdots\)
7840.2.a.w 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
7840.2.a.x 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(2\) \(1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}+3q^{11}-q^{13}+\cdots\)
7840.2.a.y 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(3\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+6q^{9}-3q^{11}-q^{13}+\cdots\)
7840.2.a.z 7840.a 1.a $1$ $62.603$ \(\Q\) None \(0\) \(3\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+6q^{9}-q^{11}+q^{13}+\cdots\)
7840.2.a.ba 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
7840.2.a.bb 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}-2\beta q^{9}+(2-2\beta )q^{11}+\cdots\)
7840.2.a.bc 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+(1+\beta )q^{9}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
7840.2.a.bd 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(1+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
7840.2.a.be 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+2q^{9}-\beta q^{11}+q^{13}+\cdots\)
7840.2.a.bf 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots\)
7840.2.a.bg 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+2q^{9}+\beta q^{11}-q^{13}+\cdots\)
7840.2.a.bh 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
7840.2.a.bi 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(1+\beta )q^{9}+(-4+\beta )q^{11}+\cdots\)
7840.2.a.bj 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+2\beta q^{9}+(2+2\beta )q^{11}+\cdots\)
7840.2.a.bk 7840.a 1.a $2$ $62.603$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+2\beta q^{9}+(-2-2\beta )q^{11}+\cdots\)
7840.2.a.bl 7840.a 1.a $3$ $62.603$ 3.3.229.1 None \(0\) \(-2\) \(-3\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bm 7840.a 1.a $3$ $62.603$ 3.3.229.1 None \(0\) \(-2\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bn 7840.a 1.a $3$ $62.603$ 3.3.229.1 None \(0\) \(2\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bo 7840.a 1.a $3$ $62.603$ 3.3.229.1 None \(0\) \(2\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+q^{5}+(2-\beta _{1}+2\beta _{2})q^{9}+\cdots\)
7840.2.a.bp 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+2\beta _{1}q^{11}+(-1-\beta _{3})q^{13}+\cdots\)
7840.2.a.bq 7840.a 1.a $4$ $62.603$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(\beta _{1}+\beta _{3})q^{11}+(3-\beta _{2}+\cdots)q^{13}+\cdots\)
7840.2.a.br 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
7840.2.a.bs 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
7840.2.a.bt 7840.a 1.a $4$ $62.603$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(\beta _{1}-\beta _{3})q^{11}+(-3+\cdots)q^{13}+\cdots\)
7840.2.a.bu 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-2\beta _{1}q^{11}+(1-\beta _{3})q^{13}+\cdots\)
7840.2.a.bv 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+\beta _{3}q^{11}+\cdots\)
7840.2.a.bw 7840.a 1.a $4$ $62.603$ \(\Q(\sqrt{5}, \sqrt{13})\) None \(0\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
7840.2.a.bx 7840.a 1.a $5$ $62.603$ 5.5.1686096.1 None \(0\) \(0\) \(-5\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+(-1-\beta _{4})q^{11}+\cdots\)
7840.2.a.by 7840.a 1.a $5$ $62.603$ 5.5.1686096.1 None \(0\) \(0\) \(-5\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{9}+(1+\beta _{4})q^{11}+\cdots\)
7840.2.a.bz 7840.a 1.a $5$ $62.603$ 5.5.1686096.1 None \(0\) \(0\) \(5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+(-1-\beta _{4})q^{11}+\cdots\)
7840.2.a.ca 7840.a 1.a $5$ $62.603$ 5.5.1686096.1 None \(0\) \(0\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{9}+(1+\beta _{4})q^{11}+\cdots\)
7840.2.a.cb 7840.a 1.a $6$ $62.603$ 6.6.28198912.1 None \(0\) \(-4\) \(-6\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7840.2.a.cc 7840.a 1.a $6$ $62.603$ 6.6.28198912.1 None \(0\) \(-4\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(2-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
7840.2.a.cd 7840.a 1.a $6$ $62.603$ 6.6.170145936.1 None \(0\) \(0\) \(-6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-q^{5}+(2-\beta _{5})q^{9}+\beta _{2}q^{11}+\cdots\)
7840.2.a.ce 7840.a 1.a $6$ $62.603$ 6.6.170145936.1 None \(0\) \(0\) \(6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+q^{5}+(2-\beta _{5})q^{9}-\beta _{2}q^{11}+\cdots\)
7840.2.a.cf 7840.a 1.a $6$ $62.603$ 6.6.28198912.1 None \(0\) \(4\) \(-6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(2-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
7840.2.a.cg 7840.a 1.a $6$ $62.603$ 6.6.28198912.1 None \(0\) \(4\) \(6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(2-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
7840.2.a.ch 7840.a 1.a $8$ $62.603$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(-8\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{6}q^{3}-q^{5}+(1-\beta _{2})q^{9}+(-\beta _{4}+\cdots)q^{11}+\cdots\)
7840.2.a.ci 7840.a 1.a $8$ $62.603$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(8\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{6}q^{3}+q^{5}+(1-\beta _{2})q^{9}+(\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7840))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7840)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3920))\)\(^{\oplus 2}\)