Properties

Label 1001.2.cr
Level $1001$
Weight $2$
Character orbit 1001.cr
Rep. character $\chi_{1001}(9,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $864$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.cr (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1001 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(224\)

Dimensions

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

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

Trace form

\( 864 q + 3 q^{2} - 6 q^{3} + 107 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 16 q^{8} - 194 q^{9} + O(q^{10}) \) \( 864 q + 3 q^{2} - 6 q^{3} + 107 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 16 q^{8} - 194 q^{9} - 96 q^{10} + 4 q^{11} - 8 q^{12} - 12 q^{13} - 26 q^{14} - 18 q^{15} + 91 q^{16} - 19 q^{17} - 12 q^{18} + 2 q^{19} - 30 q^{20} - 42 q^{21} + 22 q^{22} + 8 q^{23} + 70 q^{24} + 86 q^{25} - 27 q^{26} - 12 q^{27} - 51 q^{28} - 8 q^{29} - 74 q^{30} - 6 q^{31} - 16 q^{32} + 104 q^{33} - 40 q^{34} + 35 q^{35} + 129 q^{36} + 15 q^{37} + 16 q^{38} - 39 q^{39} - 38 q^{40} - 48 q^{41} - 25 q^{42} - 16 q^{43} - 24 q^{44} + 60 q^{45} + 35 q^{46} - 24 q^{47} + 30 q^{48} - 21 q^{49} + 5 q^{50} - 38 q^{51} - 15 q^{52} + 8 q^{53} + 40 q^{54} - 12 q^{55} + 58 q^{56} - 12 q^{57} - 46 q^{58} - 21 q^{59} + 94 q^{60} - 30 q^{61} - 42 q^{62} + 102 q^{63} - 236 q^{64} + 38 q^{65} - 13 q^{66} + 96 q^{67} - 89 q^{68} - 40 q^{69} - 121 q^{70} + 68 q^{71} - 82 q^{72} + 3 q^{73} - 17 q^{74} - 7 q^{75} - 16 q^{76} - 16 q^{77} + 14 q^{78} + 14 q^{79} - 126 q^{80} - 150 q^{81} - 6 q^{82} - 96 q^{83} + 100 q^{84} - 16 q^{85} + 34 q^{86} + 164 q^{87} + 56 q^{88} + 22 q^{89} - 86 q^{90} + 47 q^{91} - 60 q^{92} - 9 q^{93} + 18 q^{94} + 31 q^{95} - 24 q^{96} + 28 q^{97} - 152 q^{98} + 16 q^{99} + O(q^{100}) \)

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

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