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Properties

Label 1001.2.bg
Level $1001$
Weight $2$
Character orbit 1001.bg
Rep. character $\chi_{1001}(309,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.bg (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 232 144 88
Cusp forms 216 144 72
Eisenstein series 16 0 16

Trace form

\( 144 q + 76 q^{4} + 36 q^{6} - 80 q^{9} + O(q^{10}) \) \( 144 q + 76 q^{4} + 36 q^{6} - 80 q^{9} - 8 q^{10} - 24 q^{12} + 4 q^{13} + 16 q^{14} - 84 q^{16} + 12 q^{17} + 24 q^{20} - 4 q^{22} + 24 q^{23} + 72 q^{24} - 144 q^{25} + 8 q^{26} - 48 q^{27} - 8 q^{30} - 72 q^{32} + 4 q^{35} + 88 q^{36} + 84 q^{37} - 8 q^{38} + 24 q^{39} - 48 q^{40} - 60 q^{41} - 8 q^{42} + 4 q^{43} + 24 q^{46} + 4 q^{48} + 72 q^{49} - 24 q^{50} + 8 q^{51} - 40 q^{52} + 48 q^{53} + 48 q^{54} + 24 q^{56} + 72 q^{58} + 48 q^{59} - 28 q^{61} - 12 q^{62} - 24 q^{63} - 104 q^{64} - 40 q^{65} - 24 q^{67} - 52 q^{68} - 8 q^{69} - 12 q^{71} + 36 q^{72} + 36 q^{74} - 20 q^{75} - 16 q^{77} + 36 q^{78} - 56 q^{79} + 144 q^{80} - 120 q^{81} + 28 q^{82} - 84 q^{84} + 84 q^{85} - 48 q^{87} - 12 q^{89} - 160 q^{90} - 16 q^{91} - 16 q^{92} + 24 q^{93} - 88 q^{94} - 12 q^{95} - 36 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)