Properties

Label 8880.2.a
Level $8880$
Weight $2$
Character orbit 8880.a
Rep. character $\chi_{8880}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $67$
Sturm bound $3648$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 8880 = 2^{4} \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8880.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 67 \)
Sturm bound: \(3648\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8880))\).

Total New Old
Modular forms 1848 144 1704
Cusp forms 1801 144 1657
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.

\(2\)\(3\)\(5\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(66\)
Minus space\(-\)\(78\)

Trace form

\( 144q + 144q^{9} + O(q^{10}) \) \( 144q + 144q^{9} - 4q^{15} - 8q^{19} + 144q^{25} - 8q^{31} + 24q^{43} + 48q^{47} + 144q^{49} - 8q^{51} - 32q^{53} - 16q^{55} + 16q^{59} - 16q^{61} + 16q^{69} - 32q^{71} - 32q^{77} + 40q^{79} + 144q^{81} + 16q^{85} - 24q^{87} - 32q^{89} - 80q^{91} - 32q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8880))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 37
8880.2.a.a \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8880.2.a.b \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
8880.2.a.c \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}-2q^{7}+q^{9}-q^{13}+q^{15}+\cdots\)
8880.2.a.d \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}+5q^{11}+2q^{13}+\cdots\)
8880.2.a.e \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
8880.2.a.f \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}-7q^{13}+\cdots\)
8880.2.a.g \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}-3q^{11}+2q^{13}+\cdots\)
8880.2.a.h \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+2q^{7}+q^{9}-4q^{11}+5q^{13}+\cdots\)
8880.2.a.i \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(-1\) \(5\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+5q^{7}+q^{9}+5q^{11}-q^{13}+\cdots\)
8880.2.a.j \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}+3q^{13}+\cdots\)
8880.2.a.k \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(1\) \(-2\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-2q^{7}+q^{9}-q^{13}-q^{15}+\cdots\)
8880.2.a.l \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+q^{7}+q^{9}-3q^{11}+6q^{13}+\cdots\)
8880.2.a.m \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(1\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+2q^{7}+q^{9}-3q^{13}-q^{15}+\cdots\)
8880.2.a.n \(1\) \(70.907\) \(\Q\) None \(0\) \(-1\) \(1\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+4q^{7}+q^{9}-6q^{11}+2q^{13}+\cdots\)
8880.2.a.o \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8880.2.a.p \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}+3q^{11}-5q^{13}+\cdots\)
8880.2.a.q \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}-3q^{7}+q^{9}+3q^{11}-3q^{13}+\cdots\)
8880.2.a.r \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+5q^{13}+\cdots\)
8880.2.a.s \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}-q^{7}+q^{9}+q^{11}+2q^{13}+\cdots\)
8880.2.a.t \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\)
8880.2.a.u \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{9}-2q^{13}-q^{15}-2q^{17}+\cdots\)
8880.2.a.v \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
8880.2.a.w \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
8880.2.a.x \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
8880.2.a.y \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
8880.2.a.z \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(1\) \(-3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
8880.2.a.ba \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
8880.2.a.bb \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}+6q^{13}+q^{15}+2q^{17}+\cdots\)
8880.2.a.bc \(1\) \(70.907\) \(\Q\) None \(0\) \(1\) \(1\) \(3\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}+5q^{11}-2q^{13}+\cdots\)
8880.2.a.bd \(2\) \(70.907\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}-q^{7}+q^{9}-\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
8880.2.a.be \(2\) \(70.907\) \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
8880.2.a.bf \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) \(-\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+(5-\beta )q^{11}+\cdots\)
8880.2.a.bg \(2\) \(70.907\) \(\Q(\sqrt{17}) \) None \(0\) \(-2\) \(-2\) \(3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
8880.2.a.bh \(2\) \(70.907\) \(\Q(\sqrt{113}) \) None \(0\) \(-2\) \(2\) \(-6\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}-3q^{7}+q^{9}+q^{11}+(1+\cdots)q^{13}+\cdots\)
8880.2.a.bi \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(1-2\beta )q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
8880.2.a.bj \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(3-3\beta )q^{11}+\cdots\)
8880.2.a.bk \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(4\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(1+2\beta )q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots\)
8880.2.a.bl \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(6\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+3q^{7}+q^{9}+(4-3\beta )q^{11}+\cdots\)
8880.2.a.bm \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}+(-2+\cdots)q^{11}+\cdots\)
8880.2.a.bn \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(1-2\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
8880.2.a.bo \(2\) \(70.907\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+\beta q^{11}+q^{13}+\cdots\)
8880.2.a.bp \(2\) \(70.907\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+q^{7}+q^{9}+(1+2\beta )q^{11}+\cdots\)
8880.2.a.bq \(2\) \(70.907\) \(\Q(\sqrt{109}) \) None \(0\) \(2\) \(-2\) \(6\) \(-\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+3q^{7}+q^{9}+(-1+\beta )q^{11}+\cdots\)
8880.2.a.br \(2\) \(70.907\) \(\Q(\sqrt{33}) \) None \(0\) \(2\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
8880.2.a.bs \(2\) \(70.907\) \(\Q(\sqrt{17}) \) None \(0\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+2\beta q^{7}+q^{9}+4q^{11}+\cdots\)
8880.2.a.bt \(2\) \(70.907\) \(\Q(\sqrt{13}) \) None \(0\) \(2\) \(2\) \(6\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+3q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
8880.2.a.bu \(3\) \(70.907\) 3.3.621.1 None \(0\) \(-3\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.bv \(3\) \(70.907\) 3.3.469.1 None \(0\) \(-3\) \(-3\) \(2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.bw \(3\) \(70.907\) 3.3.229.1 None \(0\) \(-3\) \(-3\) \(3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{7}+q^{9}+(1-2\beta _{1}+\beta _{2})q^{11}+\cdots\)
8880.2.a.bx \(3\) \(70.907\) 3.3.229.1 None \(0\) \(-3\) \(3\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
8880.2.a.by \(3\) \(70.907\) 3.3.2429.1 None \(0\) \(3\) \(-3\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
8880.2.a.bz \(3\) \(70.907\) 3.3.621.1 None \(0\) \(3\) \(3\) \(-6\) \(-\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+(-2+\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.ca \(3\) \(70.907\) 3.3.469.1 None \(0\) \(3\) \(3\) \(-4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(-2+\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
8880.2.a.cb \(3\) \(70.907\) 3.3.229.1 None \(0\) \(3\) \(3\) \(-3\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}-q^{7}+q^{9}+(\beta _{1}-2\beta _{2})q^{11}+\cdots\)
8880.2.a.cc \(3\) \(70.907\) 3.3.2677.1 None \(0\) \(3\) \(3\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{7}+q^{9}+\beta _{1}q^{11}+(-1+\cdots)q^{13}+\cdots\)
8880.2.a.cd \(3\) \(70.907\) 3.3.1101.1 None \(0\) \(3\) \(3\) \(4\) \(-\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(1-\beta _{2})q^{7}+q^{9}-\beta _{1}q^{11}+\cdots\)
8880.2.a.ce \(4\) \(70.907\) 4.4.40293.1 None \(0\) \(-4\) \(-4\) \(-3\) \(+\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
8880.2.a.cf \(4\) \(70.907\) 4.4.39605.1 None \(0\) \(-4\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1+\beta _{3})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.cg \(4\) \(70.907\) 4.4.54764.1 None \(0\) \(-4\) \(4\) \(-4\) \(-\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
8880.2.a.ch \(4\) \(70.907\) 4.4.119893.1 None \(0\) \(4\) \(-4\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+\beta _{3}q^{7}+q^{9}+(-2-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.ci \(4\) \(70.907\) 4.4.48389.1 None \(0\) \(4\) \(4\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+(-\beta _{1}-\beta _{3})q^{7}+q^{9}+\cdots\)
8880.2.a.cj \(5\) \(70.907\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-5\) \(-5\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{3}-q^{5}+(-1+\beta _{1})q^{7}+q^{9}-\beta _{3}q^{11}+\cdots\)
8880.2.a.ck \(5\) \(70.907\) 5.5.13350941.1 None \(0\) \(-5\) \(5\) \(-7\) \(+\) \(+\) \(-\) \(-\) \(q-q^{3}+q^{5}+(-1+\beta _{2})q^{7}+q^{9}+\beta _{4}q^{11}+\cdots\)
8880.2.a.cl \(5\) \(70.907\) 5.5.20193189.1 None \(0\) \(5\) \(-5\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q+q^{3}-q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{1}-\beta _{4})q^{11}+\cdots\)
8880.2.a.cm \(5\) \(70.907\) 5.5.600268.1 None \(0\) \(5\) \(-5\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{3}-q^{5}+(-\beta _{3}+\beta _{4})q^{7}+q^{9}+\cdots\)
8880.2.a.cn \(5\) \(70.907\) 5.5.15147037.1 None \(0\) \(5\) \(5\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}-\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
8880.2.a.co \(6\) \(70.907\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-6\) \(6\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{3}+q^{5}+\beta _{1}q^{7}+q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(222))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(444))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1776))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4440))\)\(^{\oplus 2}\)