Properties

Label 402.2.j
Level 402
Weight 2
Character orbit j
Rep. character \(\chi_{402}(5,\cdot)\)
Character field \(\Q(\zeta_{22})\)
Dimension 240
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.j (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q(\zeta_{22})\)
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 720 240 480
Cusp forms 640 240 400
Eisenstein series 80 0 80

Trace form

\( 240q - 24q^{4} + 2q^{6} - 10q^{9} + O(q^{10}) \) \( 240q - 24q^{4} + 2q^{6} - 10q^{9} + 11q^{12} + 8q^{15} - 24q^{16} - 4q^{19} - 22q^{21} + 12q^{22} - 20q^{24} - 48q^{25} - 44q^{31} + 22q^{33} - 10q^{36} + 44q^{37} + 54q^{39} + 44q^{43} - 22q^{45} - 22q^{48} + 4q^{49} - 66q^{52} - 10q^{54} - 72q^{55} - 44q^{58} + 8q^{60} + 44q^{61} - 24q^{64} - 28q^{67} + 44q^{70} - 158q^{73} + 99q^{75} - 4q^{76} - 154q^{79} - 66q^{81} - 38q^{82} - 66q^{87} + 12q^{88} - 4q^{90} + 16q^{91} - 42q^{93} - 44q^{94} + 2q^{96} + 110q^{99} + O(q^{100}) \)

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.j.a \(120\) \(3.210\) None \(-12\) \(1\) \(0\) \(0\)
402.2.j.b \(120\) \(3.210\) None \(12\) \(-1\) \(0\) \(0\)

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

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