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Properties

Label 1001.2.dk
Level $1001$
Weight $2$
Character orbit 1001.dk
Rep. character $\chi_{1001}(36,\cdot)$
Character field $\Q(\zeta_{30})$
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.dk (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 672 q - 84 q^{4} + 78 q^{9} + O(q^{10}) \) \( 672 q - 84 q^{4} + 78 q^{9} - 16 q^{10} + 24 q^{11} + 32 q^{12} - 22 q^{13} - 42 q^{15} + 60 q^{16} - 4 q^{17} - 2 q^{22} + 20 q^{23} - 96 q^{24} + 144 q^{25} - 24 q^{26} + 24 q^{27} - 46 q^{29} - 28 q^{30} + 30 q^{33} - 16 q^{35} - 148 q^{36} - 20 q^{38} - 26 q^{39} - 136 q^{40} - 128 q^{43} + 72 q^{46} - 80 q^{48} - 84 q^{49} + 60 q^{50} - 32 q^{51} + 66 q^{52} - 20 q^{53} - 72 q^{54} - 34 q^{55} + 192 q^{58} + 6 q^{59} + 20 q^{62} + 48 q^{64} - 80 q^{65} - 288 q^{66} + 72 q^{67} - 62 q^{68} + 60 q^{69} + 60 q^{71} - 156 q^{72} + 52 q^{74} + 8 q^{75} - 444 q^{76} + 8 q^{77} - 36 q^{78} + 88 q^{79} + 126 q^{81} + 84 q^{82} - 72 q^{84} - 48 q^{85} + 52 q^{87} + 174 q^{88} - 144 q^{89} - 8 q^{90} + 18 q^{91} + 68 q^{92} + 42 q^{93} + 80 q^{94} + 156 q^{95} - 126 q^{97} + O(q^{100}) \)

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

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