Properties

Label 2004.2.h
Level 2004
Weight 2
Character orbit h
Rep. character \(\chi_{2004}(1001,\cdot)\)
Character field \(\Q\)
Dimension 56
Newform subspaces 1
Sturm bound 672
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2004.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(672\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2004, [\chi])\).

Total New Old
Modular forms 342 56 286
Cusp forms 330 56 274
Eisenstein series 12 0 12

Trace form

\( 56q - 8q^{9} + O(q^{10}) \) \( 56q - 8q^{9} - 4q^{19} + 4q^{21} + 52q^{25} + 12q^{27} + 4q^{31} - 8q^{33} + 32q^{49} + 24q^{57} + 28q^{61} - 26q^{63} - 54q^{75} - 24q^{81} + 8q^{85} + 14q^{87} - 20q^{93} + 36q^{97} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2004, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2004.2.h.a \(56\) \(16.002\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(2004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database