Properties

Label 402.2.h
Level 402
Weight 2
Character orbit h
Rep. character \(\chi_{402}(239,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 44
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.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{6})\)
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 144 44 100
Cusp forms 128 44 84
Eisenstein series 16 0 16

Trace form

\( 44q - 22q^{4} - q^{6} - 12q^{7} + 2q^{9} + O(q^{10}) \) \( 44q - 22q^{4} - q^{6} - 12q^{7} + 2q^{9} - 3q^{12} + 12q^{13} + 8q^{15} - 22q^{16} - 3q^{18} - 6q^{19} - 6q^{21} - 24q^{22} + 2q^{24} + 20q^{25} + 12q^{28} - 6q^{30} + 48q^{31} - 6q^{33} + 6q^{34} - q^{36} - 20q^{37} - 12q^{39} - 60q^{46} + 3q^{48} + 54q^{49} - 3q^{51} - 28q^{54} - 20q^{55} - 3q^{57} - 4q^{60} - 12q^{61} - 42q^{63} + 44q^{64} - 40q^{67} + 30q^{69} - 18q^{73} + 12q^{76} + 48q^{78} - 24q^{79} + 82q^{81} - 56q^{82} - 6q^{84} + 60q^{85} + 18q^{87} + 12q^{88} + 26q^{90} - 8q^{91} - 18q^{93} - q^{96} + 138q^{97} - 78q^{99} + O(q^{100}) \)

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.h.a \(22\) \(3.210\) None \(-11\) \(1\) \(0\) \(-6\)
402.2.h.b \(22\) \(3.210\) None \(11\) \(-1\) \(0\) \(-6\)

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

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