Properties

Label 98.2.g
Level $98$
Weight $2$
Character orbit 98.g
Rep. character $\chi_{98}(9,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $48$
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.g (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
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 192 48 144
Cusp forms 144 48 96
Eisenstein series 48 0 48

Trace form

\( 48q + 4q^{4} - 14q^{6} - 14q^{9} + O(q^{10}) \) \( 48q + 4q^{4} - 14q^{6} - 14q^{9} - 18q^{11} + 2q^{15} + 4q^{16} - 14q^{17} - 4q^{18} - 14q^{19} - 14q^{20} - 6q^{22} - 50q^{23} - 4q^{25} - 14q^{26} - 42q^{27} + 2q^{29} - 8q^{30} - 14q^{35} - 14q^{36} - 4q^{37} + 28q^{38} + 16q^{39} + 28q^{40} + 56q^{41} - 42q^{42} + 16q^{43} + 24q^{44} + 14q^{45} + 76q^{46} - 28q^{47} + 112q^{49} + 24q^{50} + 92q^{51} - 14q^{52} - 34q^{53} + 84q^{54} + 42q^{55} + 28q^{56} - 10q^{57} - 12q^{58} + 42q^{59} + 20q^{60} + 28q^{62} - 42q^{63} - 8q^{64} - 28q^{65} - 12q^{67} - 28q^{68} - 28q^{69} - 14q^{70} + 6q^{71} - 4q^{72} - 42q^{73} - 26q^{74} - 84q^{75} - 42q^{77} - 24q^{78} - 20q^{79} - 14q^{80} + 10q^{81} - 84q^{83} - 42q^{84} + 16q^{85} - 54q^{86} + 98q^{87} - 18q^{88} - 56q^{89} - 42q^{90} - 14q^{91} + 16q^{92} + 34q^{93} - 70q^{94} + 72q^{95} - 28q^{97} - 28q^{98} - 120q^{99} + O(q^{100}) \)

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.g.a \(24\) \(0.783\) None \(-2\) \(7\) \(0\) \(0\)
98.2.g.b \(24\) \(0.783\) None \(2\) \(-7\) \(0\) \(0\)

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

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