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Properties

Label 1001.2.cv
Level $1001$
Weight $2$
Character orbit 1001.cv
Rep. character $\chi_{1001}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $672$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.cv (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1001, [\chi])\).

Total New Old
Modular forms 928 672 256
Cusp forms 864 672 192
Eisenstein series 64 0 64

Trace form

\( 672 q - 168 q^{9} + O(q^{10}) \) \( 672 q - 168 q^{9} - 20 q^{11} + 20 q^{13} + 4 q^{15} + 120 q^{16} - 60 q^{20} + 24 q^{22} + 56 q^{26} + 48 q^{27} - 48 q^{31} - 4 q^{33} + 8 q^{34} + 80 q^{39} - 52 q^{44} - 48 q^{45} - 80 q^{46} - 32 q^{47} - 224 q^{48} + 100 q^{52} + 72 q^{53} - 96 q^{55} - 80 q^{58} - 68 q^{59} - 88 q^{60} - 272 q^{66} + 56 q^{67} + 24 q^{70} + 16 q^{71} - 304 q^{78} - 160 q^{79} + 16 q^{80} - 96 q^{81} + 260 q^{83} - 80 q^{84} - 40 q^{85} - 96 q^{86} - 136 q^{89} - 64 q^{92} - 28 q^{93} + 520 q^{96} - 36 q^{97} - 68 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1001, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)