Properties

Label 402.2.d
Level 402
Weight 2
Character orbit d
Rep. character \(\chi_{402}(401,\cdot)\)
Character field \(\Q\)
Dimension 24
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 201 \)
Character field: \(\Q\)
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 72 24 48
Cusp forms 64 24 40
Eisenstein series 8 0 8

Trace form

\( 24q + 24q^{4} - 2q^{6} + 10q^{9} + O(q^{10}) \) \( 24q + 24q^{4} - 2q^{6} + 10q^{9} - 8q^{15} + 24q^{16} - 40q^{19} - 12q^{22} - 2q^{24} + 48q^{25} + 10q^{36} - 44q^{37} + 12q^{39} - 4q^{49} + 10q^{54} - 16q^{55} - 8q^{60} + 24q^{64} - 16q^{67} - 40q^{73} - 40q^{76} - 22q^{81} - 28q^{82} - 12q^{88} + 4q^{90} - 16q^{91} - 24q^{93} - 2q^{96} + O(q^{100}) \)

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.d.a \(12\) \(3.210\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(1\) \(0\) \(0\) \(q-q^{2}+\beta _{8}q^{3}+q^{4}-\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\)
402.2.d.b \(12\) \(3.210\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-1\) \(0\) \(0\) \(q+q^{2}-\beta _{8}q^{3}+q^{4}+\beta _{7}q^{5}-\beta _{8}q^{6}+\cdots\)

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

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