Properties

Label 363.2.m
Level 363
Weight 2
Character orbit m
Rep. character \(\chi_{363}(4,\cdot)\)
Character field \(\Q(\zeta_{55})\)
Dimension 880
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.m (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 121 \)
Character field: \(\Q(\zeta_{55})\)
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 1840 880 960
Cusp forms 1680 880 800
Eisenstein series 160 0 160

Trace form

\( 880q + 4q^{2} + 26q^{4} + 4q^{5} + 2q^{6} + 2q^{7} - 8q^{8} - 220q^{9} + O(q^{10}) \) \( 880q + 4q^{2} + 26q^{4} + 4q^{5} + 2q^{6} + 2q^{7} - 8q^{8} - 220q^{9} - 26q^{10} - 20q^{11} + 8q^{12} - 42q^{13} - 54q^{14} - 2q^{15} + 2q^{16} - 14q^{17} - 6q^{18} + 20q^{19} - 14q^{20} - 16q^{21} - 40q^{22} - 16q^{23} - 12q^{24} + 20q^{25} - 22q^{26} + 12q^{28} + 4q^{29} - 22q^{31} + 48q^{32} + 10q^{33} + 40q^{34} + 26q^{36} - 76q^{37} + 6q^{38} + 16q^{39} - 136q^{40} - 20q^{41} + 6q^{42} - 16q^{43} - 56q^{44} + 4q^{45} - 10q^{46} - 22q^{47} - 8q^{48} - 36q^{49} - 282q^{50} - 164q^{52} - 146q^{53} - 8q^{54} - 104q^{55} - 70q^{56} - 62q^{58} + 6q^{59} - 12q^{60} + 18q^{61} - 82q^{62} + 2q^{63} - 58q^{64} - 38q^{65} + 12q^{66} - 58q^{67} + 28q^{68} + 2q^{69} - 66q^{70} - 96q^{71} + 2q^{72} - 42q^{73} + 30q^{74} - 16q^{75} - 282q^{76} + 2q^{77} - 78q^{78} - 126q^{79} - 58q^{80} - 220q^{81} - 62q^{82} - 34q^{83} - 86q^{85} - 40q^{86} - 24q^{87} + 18q^{88} - 20q^{89} - 26q^{90} - 104q^{91} - 262q^{92} - 28q^{93} - 370q^{94} - 30q^{95} - 124q^{96} - 60q^{97} - 216q^{98} - 30q^{99} + O(q^{100}) \)

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.m.a \(440\) \(2.899\) None \(1\) \(110\) \(3\) \(-1\)
363.2.m.b \(440\) \(2.899\) None \(3\) \(-110\) \(1\) \(3\)

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