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Properties

Label 1001.2.l
Level $1001$
Weight $2$
Character orbit 1001.l
Rep. character $\chi_{1001}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $188$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 232 188 44
Cusp forms 216 188 28
Eisenstein series 16 0 16

Trace form

\( 188 q - 6 q^{3} + 192 q^{4} - 4 q^{7} - 96 q^{9} + O(q^{10}) \) \( 188 q - 6 q^{3} + 192 q^{4} - 4 q^{7} - 96 q^{9} - 16 q^{12} - 8 q^{14} - 16 q^{15} + 208 q^{16} + 8 q^{18} + 6 q^{19} - 4 q^{20} - 10 q^{21} - 8 q^{23} - 102 q^{25} + 26 q^{26} + 24 q^{27} - 40 q^{28} - 4 q^{29} + 20 q^{30} - 30 q^{31} - 40 q^{32} - 16 q^{34} - 12 q^{35} - 94 q^{36} - 40 q^{37} + 6 q^{38} + 18 q^{39} - 20 q^{40} - 86 q^{42} + 4 q^{43} - 4 q^{44} + 44 q^{46} - 12 q^{47} - 56 q^{48} + 6 q^{50} + 20 q^{51} - 88 q^{52} + 12 q^{53} + 24 q^{54} - 16 q^{55} - 30 q^{56} - 124 q^{57} + 12 q^{58} + 16 q^{59} + 4 q^{60} + 14 q^{61} + 48 q^{62} + 110 q^{63} + 208 q^{64} + 46 q^{65} - 6 q^{66} - 6 q^{67} - 40 q^{68} - 46 q^{69} + 54 q^{70} + 16 q^{71} - 32 q^{72} + 36 q^{73} - 64 q^{74} + 92 q^{75} + 16 q^{76} - 16 q^{78} - 44 q^{79} - 10 q^{80} - 70 q^{81} + 6 q^{82} + 44 q^{83} + 172 q^{84} - 24 q^{85} - 4 q^{86} - 24 q^{87} + 12 q^{88} + 16 q^{89} - 104 q^{90} + 16 q^{91} - 128 q^{92} - 20 q^{93} - 34 q^{94} + 40 q^{95} - 164 q^{96} + 52 q^{97} - 94 q^{98} + O(q^{100}) \)

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

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