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Properties

Label 1001.2.db
Level $1001$
Weight $2$
Character orbit 1001.db
Rep. character $\chi_{1001}(179,\cdot)$
Character field $\Q(\zeta_{30})$
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.db (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1001 \)
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 928 928 0
Cusp forms 864 864 0
Eisenstein series 64 64 0

Trace form

\( 864 q - 9 q^{2} - 6 q^{3} - 101 q^{4} - 18 q^{6} - 9 q^{7} - 218 q^{9} + O(q^{10}) \) \( 864 q - 9 q^{2} - 6 q^{3} - 101 q^{4} - 18 q^{6} - 9 q^{7} - 218 q^{9} - 64 q^{10} - 12 q^{13} - 22 q^{14} + 18 q^{15} + 107 q^{16} - 7 q^{17} + 18 q^{18} - 6 q^{20} + 18 q^{21} - 34 q^{22} + 8 q^{23} - 98 q^{25} + 21 q^{26} - 12 q^{27} - 9 q^{28} - 8 q^{29} - 82 q^{30} - 48 q^{32} + 3 q^{35} - 59 q^{36} - 9 q^{37} - 28 q^{38} - 51 q^{39} - 22 q^{40} + 23 q^{42} - 16 q^{43} - 36 q^{44} - 24 q^{45} - 9 q^{46} + 54 q^{47} - 34 q^{48} + 15 q^{49} - 75 q^{50} + 34 q^{51} - 23 q^{52} + 28 q^{53} + 24 q^{54} - 2 q^{55} - 18 q^{56} - 33 q^{59} - 120 q^{60} - 126 q^{61} - 58 q^{62} - 6 q^{63} + 156 q^{64} - 94 q^{65} + 7 q^{66} - 5 q^{68} - 8 q^{69} - 27 q^{70} + 24 q^{71} - 27 q^{73} + 15 q^{74} + 77 q^{75} - 96 q^{76} - 40 q^{77} + 30 q^{78} + 14 q^{79} - 54 q^{81} + 26 q^{82} + 90 q^{84} + 84 q^{85} + 12 q^{86} - 220 q^{87} - 56 q^{88} - 126 q^{89} + 114 q^{90} + 85 q^{91} - 76 q^{92} + 147 q^{93} - 78 q^{94} - 25 q^{95} - 126 q^{96} - 72 q^{97} - 24 q^{98} + O(q^{100}) \)

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.