Properties

Label 5390.2.a
Level $5390$
Weight $2$
Character orbit 5390.a
Rep. character $\chi_{5390}(1,\cdot)$
Character field $\Q$
Dimension $134$
Newform subspaces $65$
Sturm bound $2016$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5390.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 65 \)
Sturm bound: \(2016\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(3\), \(13\), \(17\), \(19\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5390))\).

Total New Old
Modular forms 1040 134 906
Cusp forms 977 134 843
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.

\(2\)\(5\)\(7\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(52\)
Minus space\(-\)\(82\)

Trace form

\( 134q - 4q^{3} + 134q^{4} - 2q^{5} - 4q^{6} + 122q^{9} + O(q^{10}) \) \( 134q - 4q^{3} + 134q^{4} - 2q^{5} - 4q^{6} + 122q^{9} - 4q^{12} - 16q^{13} + 134q^{16} + 8q^{17} - 8q^{19} - 2q^{20} + 2q^{22} + 12q^{23} - 4q^{24} + 134q^{25} + 4q^{26} - 16q^{27} - 4q^{29} - 4q^{30} - 20q^{31} - 4q^{33} - 8q^{34} + 122q^{36} + 84q^{37} + 80q^{39} + 20q^{41} + 72q^{43} + 6q^{45} - 20q^{46} - 12q^{47} - 4q^{48} - 32q^{51} - 16q^{52} - 12q^{53} - 16q^{54} + 80q^{57} - 16q^{58} + 24q^{59} - 36q^{61} + 40q^{62} + 134q^{64} + 8q^{65} + 60q^{67} + 8q^{68} + 40q^{69} - 20q^{71} - 8q^{73} - 24q^{74} - 4q^{75} - 8q^{76} + 112q^{79} - 2q^{80} + 86q^{81} + 40q^{83} - 8q^{85} - 32q^{86} + 40q^{87} + 2q^{88} + 16q^{89} + 12q^{92} + 80q^{93} + 28q^{94} - 8q^{95} - 4q^{96} + 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5390))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 7 11
5390.2.a.a \(1\) \(43.039\) \(\Q\) None \(-1\) \(-3\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{8}+\cdots\)
5390.2.a.b \(1\) \(43.039\) \(\Q\) None \(-1\) \(-3\) \(1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\)
5390.2.a.c \(1\) \(43.039\) \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
5390.2.a.d \(1\) \(43.039\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5390.2.a.e \(1\) \(43.039\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5390.2.a.f \(1\) \(43.039\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
5390.2.a.g \(1\) \(43.039\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5390.2.a.h \(1\) \(43.039\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
5390.2.a.i \(1\) \(43.039\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
5390.2.a.j \(1\) \(43.039\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
5390.2.a.k \(1\) \(43.039\) \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-3q^{9}+q^{10}+\cdots\)
5390.2.a.l \(1\) \(43.039\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
5390.2.a.m \(1\) \(43.039\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
5390.2.a.n \(1\) \(43.039\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5390.2.a.o \(1\) \(43.039\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5390.2.a.p \(1\) \(43.039\) \(\Q\) None \(-1\) \(1\) \(1\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
5390.2.a.q \(1\) \(43.039\) \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots\)
5390.2.a.r \(1\) \(43.039\) \(\Q\) None \(-1\) \(2\) \(1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}-q^{8}+\cdots\)
5390.2.a.s \(1\) \(43.039\) \(\Q\) None \(-1\) \(3\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-q^{5}-3q^{6}-q^{8}+\cdots\)
5390.2.a.t \(1\) \(43.039\) \(\Q\) None \(-1\) \(3\) \(1\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}-q^{8}+\cdots\)
5390.2.a.u \(1\) \(43.039\) \(\Q\) None \(1\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{8}+\cdots\)
5390.2.a.v \(1\) \(43.039\) \(\Q\) None \(1\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{8}+\cdots\)
5390.2.a.w \(1\) \(43.039\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5390.2.a.x \(1\) \(43.039\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5390.2.a.y \(1\) \(43.039\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5390.2.a.z \(1\) \(43.039\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
5390.2.a.ba \(1\) \(43.039\) \(\Q\) None \(1\) \(0\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
5390.2.a.bb \(1\) \(43.039\) \(\Q\) None \(1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
5390.2.a.bc \(1\) \(43.039\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5390.2.a.bd \(1\) \(43.039\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5390.2.a.be \(1\) \(43.039\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5390.2.a.bf \(1\) \(43.039\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
5390.2.a.bg \(1\) \(43.039\) \(\Q\) None \(1\) \(2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
5390.2.a.bh \(1\) \(43.039\) \(\Q\) None \(1\) \(2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
5390.2.a.bi \(1\) \(43.039\) \(\Q\) None \(1\) \(2\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}+q^{8}+\cdots\)
5390.2.a.bj \(1\) \(43.039\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
5390.2.a.bk \(2\) \(43.039\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
5390.2.a.bl \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
5390.2.a.bm \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
5390.2.a.bn \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
5390.2.a.bo \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{8}+\cdots\)
5390.2.a.bp \(2\) \(43.039\) \(\Q(\sqrt{33}) \) None \(-2\) \(1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
5390.2.a.bq \(2\) \(43.039\) \(\Q(\sqrt{33}) \) None \(2\) \(-4\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
5390.2.a.br \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(2\) \(-4\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
5390.2.a.bs \(2\) \(43.039\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5390.2.a.bt \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+q^{8}+\cdots\)
5390.2.a.bu \(2\) \(43.039\) \(\Q(\sqrt{2}) \) None \(2\) \(4\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(2+\beta )q^{6}+\cdots\)
5390.2.a.bv \(3\) \(43.039\) \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5390.2.a.bw \(3\) \(43.039\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
5390.2.a.bx \(3\) \(43.039\) \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.by \(3\) \(43.039\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(3\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
5390.2.a.bz \(3\) \(43.039\) 3.3.892.1 None \(-3\) \(0\) \(3\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5390.2.a.ca \(3\) \(43.039\) 3.3.316.1 None \(3\) \(-2\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5390.2.a.cb \(4\) \(43.039\) 4.4.14336.1 None \(-4\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.cc \(4\) \(43.039\) 4.4.14336.1 None \(-4\) \(0\) \(4\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.cd \(4\) \(43.039\) 4.4.7168.1 None \(4\) \(-4\) \(4\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
5390.2.a.ce \(4\) \(43.039\) 4.4.43449.1 None \(4\) \(-1\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.cf \(4\) \(43.039\) 4.4.43449.1 None \(4\) \(1\) \(4\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
5390.2.a.cg \(4\) \(43.039\) 4.4.7168.1 None \(4\) \(4\) \(-4\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
5390.2.a.ch \(5\) \(43.039\) 5.5.12760689.1 None \(5\) \(0\) \(-5\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5390.2.a.ci \(5\) \(43.039\) 5.5.12760689.1 None \(5\) \(0\) \(5\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.cj \(6\) \(43.039\) 6.6.30728192.1 None \(-6\) \(0\) \(-6\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
5390.2.a.ck \(6\) \(43.039\) 6.6.30728192.1 None \(-6\) \(0\) \(6\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
5390.2.a.cl \(6\) \(43.039\) 6.6.27410432.1 None \(6\) \(-4\) \(-6\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
5390.2.a.cm \(6\) \(43.039\) 6.6.27410432.1 None \(6\) \(4\) \(6\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+q^{5}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5390))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5390)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2695))\)\(^{\oplus 2}\)