Properties

Label 402.2.n
Level 402
Weight 2
Character orbit n
Rep. character \(\chi_{402}(11,\cdot)\)
Character field \(\Q(\zeta_{66})\)
Dimension 440
Newform subspaces 2
Sturm bound 136
Trace bound 2

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Defining parameters

Level: \( N \) \(=\) \( 402 = 2 \cdot 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 402.n (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 201 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 2 \)
Sturm bound: \(136\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(402, [\chi])\).

Total New Old
Modular forms 1440 440 1000
Cusp forms 1280 440 840
Eisenstein series 160 0 160

Trace form

\( 440q + 22q^{4} + q^{6} + 12q^{7} - 2q^{9} + O(q^{10}) \) \( 440q + 22q^{4} + q^{6} + 12q^{7} - 2q^{9} - 8q^{12} - 12q^{13} - 8q^{15} + 22q^{16} + 3q^{18} + 50q^{19} + 28q^{21} + 24q^{22} + 20q^{24} - 20q^{25} - 12q^{28} + 6q^{30} - 4q^{31} - 16q^{33} - 6q^{34} + q^{36} + 20q^{37} - 54q^{39} - 44q^{43} + 22q^{45} + 60q^{46} + 19q^{48} - 54q^{49} + 3q^{51} + 44q^{52} + 28q^{54} - 288q^{55} + 3q^{57} - 88q^{58} + 4q^{60} - 296q^{61} + 42q^{63} - 44q^{64} - 48q^{67} - 30q^{69} - 308q^{70} - 334q^{73} - 99q^{75} - 100q^{76} - 48q^{78} + 24q^{79} + 6q^{81} - 76q^{82} + 6q^{84} - 60q^{85} + 48q^{87} - 12q^{88} - 26q^{90} + 8q^{91} + 84q^{93} + 44q^{94} + q^{96} - 138q^{97} - 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(402, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
402.2.n.a \(220\) \(3.210\) None \(-11\) \(1\) \(0\) \(6\)
402.2.n.b \(220\) \(3.210\) None \(11\) \(-1\) \(0\) \(6\)

Decomposition of \(S_{2}^{\mathrm{old}}(402, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(402, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database