Properties

Label 4998.2.a
Level $4998$
Weight $2$
Character orbit 4998.a
Rep. character $\chi_{4998}(1,\cdot)$
Character field $\Q$
Dimension $108$
Newform subspaces $68$
Sturm bound $2016$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4998.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 68 \)
Sturm bound: \(2016\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4998))\).

Total New Old
Modular forms 1040 108 932
Cusp forms 977 108 869
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.

\(2\)\(3\)\(7\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(8\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(10\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(47\)
Minus space\(-\)\(61\)

Trace form

\( 108q - 2q^{3} + 108q^{4} - 2q^{6} + 108q^{9} + O(q^{10}) \) \( 108q - 2q^{3} + 108q^{4} - 2q^{6} + 108q^{9} - 8q^{10} - 8q^{11} - 2q^{12} + 108q^{16} - 16q^{19} - 8q^{23} - 2q^{24} + 84q^{25} - 2q^{27} - 16q^{29} - 8q^{31} - 4q^{34} + 108q^{36} + 24q^{37} + 8q^{38} + 36q^{39} - 8q^{40} - 16q^{41} + 32q^{43} - 8q^{44} + 8q^{46} - 2q^{48} + 8q^{50} + 2q^{51} + 16q^{53} - 2q^{54} + 16q^{55} + 48q^{57} + 16q^{58} + 24q^{59} + 8q^{61} + 8q^{62} + 108q^{64} - 32q^{65} + 8q^{66} + 56q^{67} + 12q^{69} + 24q^{71} + 8q^{73} - 16q^{74} - 14q^{75} - 16q^{76} + 4q^{78} + 48q^{79} + 108q^{81} + 8q^{82} - 8q^{83} + 8q^{85} - 16q^{86} + 16q^{87} - 8q^{90} - 8q^{92} + 36q^{93} + 16q^{94} + 32q^{95} - 2q^{96} - 8q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4998))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 17
4998.2.a.a \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.b \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.c \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.d \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
4998.2.a.e \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.f \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.g \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.h \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.i \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.j \(1\) \(39.909\) \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.k \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-3\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.l \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.m \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.n \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.o \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.p \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.q \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.r \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.s \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.t \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.u \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.v \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(2\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.w \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(3\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.x \(1\) \(39.909\) \(\Q\) None \(-1\) \(1\) \(4\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}-q^{8}+\cdots\)
4998.2.a.y \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.z \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.ba \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bb \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bc \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bd \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(1\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.be \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bf \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bg \(1\) \(39.909\) \(\Q\) None \(1\) \(-1\) \(3\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bh \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bi \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bj \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-3\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bk \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bl \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bm \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bn \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(-1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bo \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bp \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bq \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(2\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.br \(1\) \(39.909\) \(\Q\) None \(1\) \(1\) \(3\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.bs \(2\) \(39.909\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(-1\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.bt \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.bu \(2\) \(39.909\) \(\Q(\sqrt{33}) \) None \(-2\) \(-2\) \(3\) \(0\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.bv \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.bw \(2\) \(39.909\) \(\Q(\sqrt{6}) \) None \(2\) \(-2\) \(-4\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bx \(2\) \(39.909\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.by \(2\) \(39.909\) \(\Q(\sqrt{57}) \) None \(2\) \(-2\) \(-2\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.bz \(2\) \(39.909\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}-q^{6}+\cdots\)
4998.2.a.ca \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2\beta q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cb \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cc \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cd \(2\) \(39.909\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots\)
4998.2.a.ce \(2\) \(39.909\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2\beta q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cf \(2\) \(39.909\) \(\Q(\sqrt{57}) \) None \(2\) \(2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.cg \(3\) \(39.909\) 3.3.1944.1 None \(-3\) \(-3\) \(-3\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
4998.2.a.ch \(3\) \(39.909\) 3.3.1944.1 None \(-3\) \(3\) \(3\) \(0\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\)
4998.2.a.ci \(3\) \(39.909\) 3.3.469.1 None \(3\) \(-3\) \(-1\) \(0\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+q^{8}+\cdots\)
4998.2.a.cj \(3\) \(39.909\) 3.3.469.1 None \(3\) \(3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{2}q^{5}+q^{6}+q^{8}+\cdots\)
4998.2.a.ck \(4\) \(39.909\) 4.4.10304.1 None \(-4\) \(-4\) \(-2\) \(0\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)
4998.2.a.cl \(4\) \(39.909\) 4.4.31808.1 None \(-4\) \(-4\) \(2\) \(0\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}-q^{8}+\cdots\)
4998.2.a.cm \(4\) \(39.909\) 4.4.31808.1 None \(-4\) \(4\) \(-2\) \(0\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
4998.2.a.cn \(4\) \(39.909\) 4.4.10304.1 None \(-4\) \(4\) \(2\) \(0\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
4998.2.a.co \(4\) \(39.909\) 4.4.16448.2 None \(4\) \(-4\) \(-2\) \(0\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
4998.2.a.cp \(4\) \(39.909\) 4.4.16448.2 None \(4\) \(4\) \(2\) \(0\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4998))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4998)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(714))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2499))\)\(^{\oplus 2}\)