Properties

Label 363.2.i
Level 363
Weight 2
Character orbit i
Rep. character \(\chi_{363}(34,\cdot)\)
Character field \(\Q(\zeta_{11})\)
Dimension 220
Newform subspaces 2
Sturm bound 88
Trace bound 2

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Defining parameters

Level: \( N \) = \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 363.i (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).

Total New Old
Modular forms 460 220 240
Cusp forms 420 220 200
Eisenstein series 40 0 40

Trace form

\( 220q - 4q^{2} - 26q^{4} - 4q^{5} - 2q^{6} - 12q^{7} - 12q^{8} + 220q^{9} + O(q^{10}) \) \( 220q - 4q^{2} - 26q^{4} - 4q^{5} - 2q^{6} - 12q^{7} - 12q^{8} + 220q^{9} + 6q^{10} + 10q^{11} - 8q^{12} + 32q^{13} + 24q^{14} - 8q^{15} - 42q^{16} - 16q^{17} - 4q^{18} - 20q^{19} - 36q^{20} - 4q^{21} + 10q^{22} + 16q^{23} - 18q^{24} - 50q^{25} - 28q^{26} - 52q^{28} - 24q^{29} - 20q^{30} + 2q^{31} - 68q^{32} - 10q^{33} - 40q^{34} - 40q^{35} - 26q^{36} + 26q^{37} - 56q^{38} - 16q^{39} + 36q^{40} - 40q^{41} - 16q^{42} - 44q^{43} - 54q^{44} - 4q^{45} - 80q^{46} - 48q^{47} - 32q^{48} - 34q^{49} + 172q^{50} - 20q^{51} + 54q^{52} + 76q^{53} - 2q^{54} + 24q^{55} + 70q^{56} - 20q^{57} + 2q^{58} - 36q^{59} - 28q^{60} - 68q^{61} + 22q^{62} - 12q^{63} - 82q^{64} - 22q^{65} - 32q^{66} + 58q^{67} - 128q^{68} - 12q^{69} - 64q^{70} + 36q^{71} - 12q^{72} - 38q^{73} - 120q^{74} - 24q^{75} + 102q^{76} - 92q^{77} + 78q^{78} + 56q^{79} - 152q^{80} + 220q^{81} - 48q^{82} - 96q^{83} - 60q^{84} - 24q^{85} - 100q^{86} - 36q^{87} - 118q^{88} + 20q^{89} + 6q^{90} - 6q^{91} + 92q^{92} - 32q^{93} + 200q^{94} - 120q^{95} + 74q^{96} - 10q^{97} - 4q^{98} + 10q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
363.2.i.a \(110\) \(2.899\) None \(-3\) \(110\) \(-6\) \(-8\)
363.2.i.b \(110\) \(2.899\) None \(-1\) \(-110\) \(2\) \(-4\)

Decomposition of \(S_{2}^{\mathrm{old}}(363, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(363, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database