Properties

Label 5520.2.a
Level $5520$
Weight $2$
Character orbit 5520.a
Rep. character $\chi_{5520}(1,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $55$
Sturm bound $2304$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5520.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 55 \)
Sturm bound: \(2304\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5520))\).

Total New Old
Modular forms 1176 88 1088
Cusp forms 1129 88 1041
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.

\(2\)\(3\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(+\)\(-\)\(-\)$+$\(6\)
\(+\)\(-\)\(+\)\(+\)$-$\(8\)
\(+\)\(-\)\(+\)\(-\)$+$\(4\)
\(+\)\(-\)\(-\)\(+\)$+$\(4\)
\(+\)\(-\)\(-\)\(-\)$-$\(8\)
\(-\)\(+\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(+\)\(-\)$+$\(5\)
\(-\)\(+\)\(-\)\(+\)$+$\(5\)
\(-\)\(+\)\(-\)\(-\)$-$\(6\)
\(-\)\(-\)\(+\)\(+\)$+$\(5\)
\(-\)\(-\)\(+\)\(-\)$-$\(6\)
\(-\)\(-\)\(-\)\(+\)$-$\(6\)
\(-\)\(-\)\(-\)\(-\)$+$\(5\)
Plus space\(+\)\(40\)
Minus space\(-\)\(48\)

Trace form

\( 88 q + 4 q^{3} + 8 q^{7} + 88 q^{9} + O(q^{10}) \) \( 88 q + 4 q^{3} + 8 q^{7} + 88 q^{9} + 8 q^{19} + 88 q^{25} + 4 q^{27} + 8 q^{31} + 8 q^{39} + 8 q^{43} + 104 q^{49} - 32 q^{53} - 16 q^{55} + 16 q^{57} - 32 q^{59} - 32 q^{61} + 8 q^{63} + 8 q^{67} - 32 q^{71} + 16 q^{73} + 4 q^{75} - 32 q^{77} + 8 q^{79} + 88 q^{81} - 24 q^{87} - 64 q^{91} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5520))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 23
5520.2.a.a 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.e \(0\) \(-1\) \(-1\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
5520.2.a.b 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.b \(0\) \(-1\) \(-1\) \(-4\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}-2q^{13}+\cdots\)
5520.2.a.c 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.i \(0\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-3q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
5520.2.a.d 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.i \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-2q^{11}+q^{15}+6q^{17}+\cdots\)
5520.2.a.e 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.h \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-2q^{13}+q^{15}-6q^{17}+\cdots\)
5520.2.a.f 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.e \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
5520.2.a.g 5520.a 1.a $1$ $44.077$ \(\Q\) None 1380.2.a.c \(0\) \(-1\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
5520.2.a.h 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.d \(0\) \(-1\) \(-1\) \(3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
5520.2.a.i 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.k \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5520.2.a.j 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.f \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
5520.2.a.k 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.k \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{11}-q^{15}+6q^{17}+\cdots\)
5520.2.a.l 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.j \(0\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
5520.2.a.m 5520.a 1.a $1$ $44.077$ \(\Q\) None 1380.2.a.e \(0\) \(-1\) \(1\) \(3\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
5520.2.a.n 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.j \(0\) \(-1\) \(1\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+3q^{7}+q^{9}+4q^{11}-q^{15}+\cdots\)
5520.2.a.o 5520.a 1.a $1$ $44.077$ \(\Q\) None 1380.2.a.d \(0\) \(-1\) \(1\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}-q^{15}+\cdots\)
5520.2.a.p 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.a \(0\) \(-1\) \(1\) \(5\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
5520.2.a.q 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.d \(0\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
5520.2.a.r 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.b \(0\) \(1\) \(-1\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}-q^{15}+\cdots\)
5520.2.a.s 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.c \(0\) \(1\) \(-1\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+6q^{11}-4q^{13}+\cdots\)
5520.2.a.t 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.b \(0\) \(1\) \(-1\) \(-3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-3q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
5520.2.a.u 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.c \(0\) \(1\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-q^{15}+\cdots\)
5520.2.a.v 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.a \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
5520.2.a.w 5520.a 1.a $1$ $44.077$ \(\Q\) None 1380.2.a.b \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-6q^{13}-q^{15}+2q^{17}+\cdots\)
5520.2.a.x 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.h \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}+6q^{13}-q^{15}+2q^{17}+\cdots\)
5520.2.a.y 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.a \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
5520.2.a.z 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.g \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}+2q^{11}-6q^{13}+\cdots\)
5520.2.a.ba 5520.a 1.a $1$ $44.077$ \(\Q\) None 1380.2.a.a \(0\) \(1\) \(-1\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+5q^{7}+q^{9}+4q^{13}-q^{15}+\cdots\)
5520.2.a.bb 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.d \(0\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}+q^{9}-2q^{11}+4q^{13}+\cdots\)
5520.2.a.bc 5520.a 1.a $1$ $44.077$ \(\Q\) None 345.2.a.f \(0\) \(1\) \(1\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
5520.2.a.bd 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.g \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
5520.2.a.be 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.f \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}+q^{9}-4q^{13}+q^{15}+\cdots\)
5520.2.a.bf 5520.a 1.a $1$ $44.077$ \(\Q\) None 2760.2.a.e \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
5520.2.a.bg 5520.a 1.a $1$ $44.077$ \(\Q\) None 690.2.a.c \(0\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
5520.2.a.bh 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None 2760.2.a.p \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+2\beta q^{11}+\cdots\)
5520.2.a.bi 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{6}) \) None 345.2.a.i \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{7}+q^{9}-\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
5520.2.a.bj 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{15}) \) None 1380.2.a.i \(0\) \(-2\) \(2\) \(-6\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-3q^{7}+q^{9}+(-1-\beta )q^{11}+\cdots\)
5520.2.a.bk 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None 2760.2.a.q \(0\) \(-2\) \(2\) \(2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}+q^{9}+(2+3\beta )q^{11}+\cdots\)
5520.2.a.bl 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{6}) \) None 1380.2.a.f \(0\) \(2\) \(-2\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
5520.2.a.bm 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None 345.2.a.h \(0\) \(2\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+2\beta )q^{7}+q^{9}+(4+\beta )q^{11}+\cdots\)
5520.2.a.bn 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None 2760.2.a.m \(0\) \(2\) \(-2\) \(3\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}-2q^{11}+\cdots\)
5520.2.a.bo 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{11}) \) None 2760.2.a.l \(0\) \(2\) \(-2\) \(6\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
5520.2.a.bp 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{3}) \) None 1380.2.a.h \(0\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-1+2\beta )q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5520.2.a.bq 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{33}) \) None 2760.2.a.o \(0\) \(2\) \(2\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-4q^{11}+(-2+\cdots)q^{13}+\cdots\)
5520.2.a.br 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None 1380.2.a.g \(0\) \(2\) \(2\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-\beta q^{7}+q^{9}-2\beta q^{11}+\cdots\)
5520.2.a.bs 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{17}) \) None 690.2.a.l \(0\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bt 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{2}) \) None 2760.2.a.n \(0\) \(2\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
5520.2.a.bu 5520.a 1.a $2$ $44.077$ \(\Q(\sqrt{3}) \) None 345.2.a.g \(0\) \(2\) \(2\) \(6\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+3q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
5520.2.a.bv 5520.a 1.a $3$ $44.077$ 3.3.3144.1 None 1380.2.a.j \(0\) \(-3\) \(-3\) \(-2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bw 5520.a 1.a $3$ $44.077$ 3.3.1436.1 None 2760.2.a.s \(0\) \(-3\) \(-3\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.bx 5520.a 1.a $3$ $44.077$ 3.3.316.1 None 2760.2.a.r \(0\) \(-3\) \(-3\) \(6\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(2-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
5520.2.a.by 5520.a 1.a $3$ $44.077$ 3.3.316.1 None 345.2.a.j \(0\) \(-3\) \(3\) \(-6\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-2-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
5520.2.a.bz 5520.a 1.a $3$ $44.077$ 3.3.568.1 None 2760.2.a.u \(0\) \(-3\) \(3\) \(-2\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
5520.2.a.ca 5520.a 1.a $3$ $44.077$ 3.3.229.1 None 2760.2.a.t \(0\) \(-3\) \(3\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(1-\beta _{2})q^{13}+\cdots\)
5520.2.a.cb 5520.a 1.a $4$ $44.077$ 4.4.54764.1 None 2760.2.a.v \(0\) \(4\) \(-4\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{3}q^{11}+\cdots\)
5520.2.a.cc 5520.a 1.a $5$ $44.077$ 5.5.20087896.1 None 2760.2.a.w \(0\) \(5\) \(5\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1-\beta _{1})q^{7}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5520)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(552))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2760))\)\(^{\oplus 2}\)