Properties

Label 6080.2.a
Level $6080$
Weight $2$
Character orbit 6080.a
Rep. character $\chi_{6080}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $64$
Sturm bound $1920$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 6080 = 2^{6} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6080.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 64 \)
Sturm bound: \(1920\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6080))\).

Total New Old
Modular forms 984 144 840
Cusp forms 937 144 793
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.

\(2\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(21\)
\(+\)\(-\)\(+\)\(-\)\(19\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(17\)
\(-\)\(-\)\(-\)\(-\)\(21\)
Plus space\(+\)\(64\)
Minus space\(-\)\(80\)

Trace form

\( 144 q + 144 q^{9} + O(q^{10}) \) \( 144 q + 144 q^{9} + 144 q^{25} + 32 q^{29} + 32 q^{37} + 144 q^{49} + 32 q^{53} + 32 q^{77} + 176 q^{81} + 32 q^{89} + 96 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6080))\) 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 19
6080.2.a.a 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-3\) \(-1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots\)
6080.2.a.b 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-3\) \(1\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+5q^{7}+6q^{9}-4q^{11}+\cdots\)
6080.2.a.c 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
6080.2.a.d 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
6080.2.a.e 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-2\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
6080.2.a.f 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
6080.2.a.g 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}-2q^{9}-5q^{13}+\cdots\)
6080.2.a.h 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-q^{7}-2q^{9}+q^{13}+q^{15}+\cdots\)
6080.2.a.i 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(-1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}+3q^{13}-q^{15}+\cdots\)
6080.2.a.j 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-4q^{11}+6q^{13}-6q^{17}+\cdots\)
6080.2.a.k 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}+4q^{11}+6q^{13}-6q^{17}+\cdots\)
6080.2.a.l 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
6080.2.a.m 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
6080.2.a.n 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}-4q^{11}+4q^{13}+\cdots\)
6080.2.a.o 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{9}+4q^{11}+4q^{13}+\cdots\)
6080.2.a.p 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(1\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}+q^{13}-q^{15}+\cdots\)
6080.2.a.q 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(1\) \(-1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+3q^{7}-2q^{9}-5q^{13}+\cdots\)
6080.2.a.r 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}-2q^{9}+3q^{13}+q^{15}+\cdots\)
6080.2.a.s 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(2\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
6080.2.a.t 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
6080.2.a.u 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(2\) \(-1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
6080.2.a.v 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(2\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
6080.2.a.w 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(3\) \(-1\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+q^{7}+6q^{9}+4q^{11}+\cdots\)
6080.2.a.x 6080.a 1.a $1$ $48.549$ \(\Q\) None \(0\) \(3\) \(1\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-5q^{7}+6q^{9}+4q^{11}+\cdots\)
6080.2.a.y 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{3}-q^{5}+(2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
6080.2.a.z 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+2q^{7}+(1-2\beta )q^{9}+\cdots\)
6080.2.a.ba 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(1-2\beta )q^{9}-2q^{11}+\cdots\)
6080.2.a.bb 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-2\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{5}+\beta q^{7}+(1+\beta )q^{9}+4q^{11}+\cdots\)
6080.2.a.bc 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(2\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}+(-2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6080.2.a.bd 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-3q^{9}-4q^{11}+(-2+\cdots)q^{13}+\cdots\)
6080.2.a.be 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-3q^{9}+4q^{11}+(-2+\cdots)q^{13}+\cdots\)
6080.2.a.bf 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-2\beta q^{7}-q^{9}+(-2+2\beta )q^{11}+\cdots\)
6080.2.a.bg 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-2\beta q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots\)
6080.2.a.bh 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-2\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
6080.2.a.bi 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(2\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
6080.2.a.bj 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}-2q^{7}+(1+2\beta )q^{9}+\cdots\)
6080.2.a.bk 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(1+2\beta )q^{9}+2q^{11}+\cdots\)
6080.2.a.bl 6080.a 1.a $2$ $48.549$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}-q^{5}+(-2+2\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
6080.2.a.bm 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(-4\) \(-3\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bn 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(-4\) \(3\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bo 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(-2\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bp 6080.a 1.a $3$ $48.549$ 3.3.564.1 None \(0\) \(-2\) \(3\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
6080.2.a.bq 6080.a 1.a $3$ $48.549$ 3.3.229.1 None \(0\) \(-1\) \(-3\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}-\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
6080.2.a.br 6080.a 1.a $3$ $48.549$ 3.3.316.1 None \(0\) \(-1\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.bs 6080.a 1.a $3$ $48.549$ 3.3.568.1 None \(0\) \(-1\) \(3\) \(5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(2+\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bt 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(0\) \(-3\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-q^{5}+(-1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.bu 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(0\) \(-3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bv 6080.a 1.a $3$ $48.549$ 3.3.229.1 None \(0\) \(1\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-q^{5}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
6080.2.a.bw 6080.a 1.a $3$ $48.549$ 3.3.568.1 None \(0\) \(1\) \(3\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
6080.2.a.bx 6080.a 1.a $3$ $48.549$ 3.3.316.1 None \(0\) \(1\) \(3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
6080.2.a.by 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(2\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.bz 6080.a 1.a $3$ $48.549$ 3.3.564.1 None \(0\) \(2\) \(3\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
6080.2.a.ca 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(4\) \(-3\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}-q^{5}+(1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.cb 6080.a 1.a $3$ $48.549$ 3.3.148.1 None \(0\) \(4\) \(3\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{1}+\beta _{2})q^{7}+\cdots\)
6080.2.a.cc 6080.a 1.a $4$ $48.549$ 4.4.11344.1 None \(0\) \(-2\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+(1-\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
6080.2.a.cd 6080.a 1.a $4$ $48.549$ 4.4.17428.1 None \(0\) \(-1\) \(-4\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
6080.2.a.ce 6080.a 1.a $4$ $48.549$ 4.4.78292.1 None \(0\) \(-1\) \(4\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{5}+(-1-\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6080.2.a.cf 6080.a 1.a $4$ $48.549$ 4.4.17428.1 None \(0\) \(1\) \(-4\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(-1-\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
6080.2.a.cg 6080.a 1.a $4$ $48.549$ 4.4.78292.1 None \(0\) \(1\) \(4\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)
6080.2.a.ch 6080.a 1.a $4$ $48.549$ 4.4.11344.1 None \(0\) \(2\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}+(-1+\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
6080.2.a.ci 6080.a 1.a $5$ $48.549$ 5.5.387268.1 None \(0\) \(-4\) \(5\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{4})q^{7}+\cdots\)
6080.2.a.cj 6080.a 1.a $5$ $48.549$ 5.5.2363492.1 None \(0\) \(-2\) \(-5\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
6080.2.a.ck 6080.a 1.a $5$ $48.549$ 5.5.2363492.1 None \(0\) \(2\) \(-5\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+\beta _{2}q^{7}+(4-\beta _{3})q^{9}+\cdots\)
6080.2.a.cl 6080.a 1.a $5$ $48.549$ 5.5.387268.1 None \(0\) \(4\) \(5\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+q^{5}+(1+\beta _{4})q^{7}+(2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6080))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6080)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1520))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3040))\)\(^{\oplus 2}\)