Properties

Label 7098.2.a
Level $7098$
Weight $2$
Character orbit 7098.a
Rep. character $\chi_{7098}(1,\cdot)$
Character field $\Q$
Dimension $154$
Newform subspaces $73$
Sturm bound $2912$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 73 \)
Sturm bound: \(2912\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7098))\).

Total New Old
Modular forms 1512 154 1358
Cusp forms 1401 154 1247
Eisenstein series 111 0 111

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(11\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(9\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(9\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(11\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(9\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(13\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(12\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(66\)
Minus space\(-\)\(88\)

Trace form

\( 154q - 2q^{2} + 154q^{4} - 4q^{5} - 2q^{8} + 154q^{9} + O(q^{10}) \) \( 154q - 2q^{2} + 154q^{4} - 4q^{5} - 2q^{8} + 154q^{9} - 4q^{10} - 8q^{11} - 8q^{15} + 154q^{16} - 4q^{17} - 2q^{18} - 4q^{20} + 2q^{21} - 16q^{23} + 134q^{25} - 12q^{29} - 16q^{31} - 2q^{32} - 20q^{34} - 8q^{35} + 154q^{36} + 20q^{37} - 4q^{40} - 4q^{41} - 2q^{42} - 8q^{43} - 8q^{44} - 4q^{45} + 8q^{46} + 16q^{47} + 154q^{49} + 2q^{50} - 28q^{53} - 16q^{55} + 24q^{57} - 4q^{58} - 32q^{59} - 8q^{60} + 12q^{61} + 32q^{62} + 154q^{64} - 4q^{68} + 8q^{70} - 2q^{72} + 28q^{73} + 4q^{74} + 32q^{75} - 16q^{77} - 16q^{79} - 4q^{80} + 154q^{81} + 12q^{82} + 16q^{83} + 2q^{84} + 40q^{85} + 24q^{86} + 12q^{89} - 4q^{90} - 16q^{92} + 32q^{93} + 16q^{94} + 16q^{95} + 44q^{97} - 2q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\) 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 13
7098.2.a.a \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.b \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.c \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.d \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.e \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.f \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(2\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.g \(1\) \(56.678\) \(\Q\) None \(-1\) \(-1\) \(4\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.h \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.i \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.j \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.k \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.l \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
7098.2.a.m \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
7098.2.a.n \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.o \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(1\) \(-1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.p \(1\) \(56.678\) \(\Q\) None \(-1\) \(1\) \(3\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.q \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.r \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.s \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.t \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(1\) \(1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.u \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.v \(1\) \(56.678\) \(\Q\) None \(1\) \(-1\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.w \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.x \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.y \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.z \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.ba \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots\)
7098.2.a.bb \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
7098.2.a.bc \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(2\) \(-1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.bd \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.be \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.bf \(1\) \(56.678\) \(\Q\) None \(1\) \(1\) \(2\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.bg \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(-3\) \(-2\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
7098.2.a.bh \(2\) \(56.678\) \(\Q(\sqrt{41}) \) None \(-2\) \(-2\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.bi \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(1\) \(-2\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.bj \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
7098.2.a.bk \(2\) \(56.678\) \(\Q(\sqrt{129}) \) None \(-2\) \(-2\) \(4\) \(2\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.bl \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.bm \(2\) \(56.678\) \(\Q(\sqrt{57}) \) None \(-2\) \(2\) \(-1\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.bn \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+2\beta q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.bo \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(-2\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.bp \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.bq \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(3\) \(2\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.br \(2\) \(56.678\) \(\Q(\sqrt{129}) \) None \(2\) \(-2\) \(-4\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.bs \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.bt \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-1\) \(2\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
7098.2.a.bu \(2\) \(56.678\) \(\Q(\sqrt{57}) \) None \(2\) \(-2\) \(1\) \(-2\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.bv \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(3\) \(2\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
7098.2.a.bw \(2\) \(56.678\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-3\) \(-2\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
7098.2.a.bx \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
7098.2.a.by \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(2\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
7098.2.a.bz \(2\) \(56.678\) \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+2\beta q^{5}+q^{6}-q^{7}+\cdots\)
7098.2.a.ca \(2\) \(56.678\) \(\Q(\sqrt{57}) \) None \(2\) \(2\) \(1\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.cb \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-3\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
7098.2.a.cc \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(-2\) \(3\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
7098.2.a.cd \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(0\) \(3\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
7098.2.a.ce \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-3\) \(4\) \(-3\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots\)
7098.2.a.cf \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(2\) \(3\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
7098.2.a.cg \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(8\) \(-3\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(3-\beta _{1})q^{5}-q^{6}+\cdots\)
7098.2.a.ch \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(-4\) \(3\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots\)
7098.2.a.ci \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
7098.2.a.cj \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(2\) \(-3\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots\)
7098.2.a.ck \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(-3\) \(3\) \(-3\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots\)
7098.2.a.cl \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-8\) \(3\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(-3-\beta _{2})q^{5}+q^{6}+\cdots\)
7098.2.a.cm \(3\) \(56.678\) \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-2\) \(-3\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
7098.2.a.cn \(4\) \(56.678\) 4.4.13968.1 None \(-4\) \(-4\) \(-6\) \(-4\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}+q^{6}+\cdots\)
7098.2.a.co \(4\) \(56.678\) 4.4.13968.1 None \(4\) \(-4\) \(6\) \(4\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(1+\beta _{3})q^{5}-q^{6}+\cdots\)
7098.2.a.cp \(6\) \(56.678\) 6.6.8569169.1 None \(-6\) \(-6\) \(3\) \(-6\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+q^{6}+\cdots\)
7098.2.a.cq \(6\) \(56.678\) 6.6.6148961.1 None \(-6\) \(6\) \(-9\) \(6\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(-2+\beta _{5})q^{5}-q^{6}+\cdots\)
7098.2.a.cr \(6\) \(56.678\) 6.6.48406561.1 None \(-6\) \(6\) \(-3\) \(-6\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots\)
7098.2.a.cs \(6\) \(56.678\) 6.6.8569169.1 None \(6\) \(-6\) \(-3\) \(6\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{5})q^{5}+\cdots\)
7098.2.a.ct \(6\) \(56.678\) 6.6.48406561.1 None \(6\) \(6\) \(3\) \(6\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{7}+\cdots\)
7098.2.a.cu \(6\) \(56.678\) 6.6.6148961.1 None \(6\) \(6\) \(9\) \(-6\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(2-\beta _{5})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7098))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7098)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3549))\)\(^{\oplus 2}\)