Properties

Label 4004.2.e
Level 4004
Weight 2
Character orbit e
Rep. character \(\chi_{4004}(3849,\cdot)\)
Character field \(\Q\)
Dimension 96
Newform subspaces 2
Sturm bound 1344
Trace bound 7

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Defining parameters

Level: \( N \) = \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4004.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(1344\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4004, [\chi])\).

Total New Old
Modular forms 684 96 588
Cusp forms 660 96 564
Eisenstein series 24 0 24

Trace form

\( 96q - 96q^{9} + O(q^{10}) \) \( 96q - 96q^{9} + 4q^{11} + 16q^{15} + 8q^{23} - 88q^{25} - 32q^{37} + 20q^{49} - 16q^{53} + 8q^{67} + 24q^{77} + 128q^{81} - 8q^{91} + 72q^{93} - 80q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4004, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4004.2.e.a \(48\) \(31.972\) None \(0\) \(0\) \(0\) \(-4\)
4004.2.e.b \(48\) \(31.972\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(4004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2002, [\chi])\)\(^{\oplus 2}\)