Properties

Label 98.2.e
Level $98$
Weight $2$
Character orbit 98.e
Rep. character $\chi_{98}(15,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $36$
Newform subspaces $2$
Sturm bound $28$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.e (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(98, [\chi])\).

Total New Old
Modular forms 96 36 60
Cusp forms 72 36 36
Eisenstein series 24 0 24

Trace form

\( 36q - 2q^{3} - 6q^{4} - 6q^{5} + 8q^{6} - 8q^{7} + O(q^{10}) \) \( 36q - 2q^{3} - 6q^{4} - 6q^{5} + 8q^{6} - 8q^{7} - 6q^{10} + 6q^{11} - 2q^{12} - 10q^{13} - 6q^{14} - 2q^{15} - 6q^{16} - 10q^{17} - 8q^{18} - 8q^{19} + 8q^{20} - 26q^{21} + 6q^{22} + 26q^{23} - 6q^{24} - 22q^{25} - 4q^{26} - 2q^{27} - 8q^{28} - 2q^{29} - 16q^{30} - 28q^{31} - 48q^{33} - 12q^{34} - 28q^{35} + 20q^{37} - 4q^{38} + 18q^{39} + 8q^{40} - 20q^{41} + 96q^{42} - 44q^{43} + 6q^{44} + 118q^{45} + 26q^{46} + 76q^{47} + 12q^{48} + 6q^{49} - 24q^{50} + 16q^{51} + 18q^{52} + 58q^{53} + 6q^{54} + 96q^{55} + 8q^{56} - 18q^{57} + 60q^{58} - 12q^{59} - 2q^{60} + 28q^{61} - 22q^{62} + 6q^{63} - 6q^{64} - 56q^{65} - 48q^{66} - 52q^{67} + 4q^{68} - 68q^{69} - 28q^{70} - 6q^{71} - 8q^{72} - 34q^{73} - 10q^{74} - 50q^{75} - 22q^{76} - 42q^{77} + 24q^{78} - 68q^{79} + 8q^{80} - 36q^{81} - 36q^{82} + 90q^{83} + 16q^{84} - 16q^{85} + 18q^{86} - 62q^{87} + 6q^{88} + 56q^{89} - 36q^{90} + 4q^{91} - 16q^{92} + 82q^{93} + 10q^{94} - 24q^{95} - 6q^{96} + 24q^{97} - 20q^{98} + 120q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(98, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
98.2.e.a \(18\) \(0.783\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(3\) \(-6\) \(-7\) \(q-\beta _{13}q^{2}+(\beta _{1}-\beta _{14})q^{3}+(-1+\beta _{8}+\cdots)q^{4}+\cdots\)
98.2.e.b \(18\) \(0.783\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(3\) \(-5\) \(0\) \(-1\) \(q-\beta _{9}q^{2}+\beta _{4}q^{3}+(-1-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(98, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(98, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)