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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\) into newform subspaces

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

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

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