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Properties

Label 1002.2.f
Level $1002$
Weight $2$
Character orbit 1002.f
Rep. character $\chi_{1002}(5,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $4592$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1002 = 2 \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1002.f (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1002, [\chi])\).

Total New Old
Modular forms 14104 4592 9512
Cusp forms 13448 4592 8856
Eisenstein series 656 0 656

Trace form

\( 4592 q + 56 q^{4} - 4 q^{6} - 4 q^{9} + O(q^{10}) \) \( 4592 q + 56 q^{4} - 4 q^{6} - 4 q^{9} - 56 q^{16} - 8 q^{18} - 8 q^{19} - 16 q^{21} + 4 q^{24} - 64 q^{25} - 12 q^{27} - 16 q^{31} - 40 q^{33} + 4 q^{36} + 20 q^{42} - 32 q^{49} + 16 q^{54} - 36 q^{57} - 16 q^{61} - 16 q^{63} + 56 q^{64} - 8 q^{66} + 8 q^{72} + 24 q^{75} + 8 q^{76} - 36 q^{81} + 16 q^{84} + 64 q^{85} + 4 q^{87} - 64 q^{93} + 40 q^{94} - 4 q^{96} + 72 q^{97} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1002, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1002, [\chi])\) into lower level spaces

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