Properties

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

Related objects

Downloads

Learn more about

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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(2004, [\chi])\) into irreducible Hecke orbits

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

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