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Properties

Label 1001.2.q
Level $1001$
Weight $2$
Character orbit 1001.q
Rep. character $\chi_{1001}(92,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $288$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.q (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 464 288 176
Cusp forms 432 288 144
Eisenstein series 32 0 32

Trace form

\( 288 q + 8 q^{2} + 12 q^{3} - 68 q^{4} + 4 q^{5} - 12 q^{6} + 4 q^{7} + 4 q^{8} - 44 q^{9} + O(q^{10}) \) \( 288 q + 8 q^{2} + 12 q^{3} - 68 q^{4} + 4 q^{5} - 12 q^{6} + 4 q^{7} + 4 q^{8} - 44 q^{9} + 16 q^{10} + 8 q^{11} - 24 q^{12} - 6 q^{14} + 20 q^{15} - 88 q^{16} + 24 q^{17} - 30 q^{18} - 36 q^{19} + 16 q^{20} - 32 q^{21} + 40 q^{22} - 8 q^{23} - 36 q^{24} - 84 q^{25} - 22 q^{28} + 16 q^{29} - 8 q^{30} - 12 q^{31} - 104 q^{32} - 12 q^{33} + 24 q^{34} - 120 q^{36} - 20 q^{37} + 64 q^{38} + 16 q^{39} - 36 q^{40} + 56 q^{41} + 80 q^{43} - 66 q^{44} - 224 q^{45} + 10 q^{46} + 48 q^{47} + 48 q^{48} - 72 q^{49} - 76 q^{50} + 60 q^{51} - 24 q^{52} + 16 q^{53} + 80 q^{54} - 32 q^{55} + 36 q^{56} + 4 q^{57} + 102 q^{58} - 80 q^{59} + 176 q^{60} - 228 q^{62} + 20 q^{63} - 76 q^{64} - 64 q^{65} + 132 q^{66} + 48 q^{67} + 112 q^{68} + 12 q^{69} + 16 q^{70} + 40 q^{71} - 110 q^{72} + 40 q^{73} + 64 q^{74} - 60 q^{75} + 72 q^{76} + 8 q^{77} - 60 q^{79} + 256 q^{80} - 60 q^{81} + 44 q^{82} - 12 q^{83} + 24 q^{84} - 8 q^{85} + 10 q^{86} + 16 q^{87} - 116 q^{88} - 24 q^{89} + 208 q^{90} + 182 q^{92} + 36 q^{93} + 12 q^{94} - 96 q^{95} + 208 q^{96} - 64 q^{97} - 12 q^{98} - 20 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 2}\)