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Properties

Label 1001.2.dv
Level $1001$
Weight $2$
Character orbit 1001.dv
Rep. character $\chi_{1001}(101,\cdot)$
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.dv (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

\( 864 q - 15 q^{2} + 107 q^{4} - 15 q^{7} + 206 q^{9} + O(q^{10}) \) \( 864 q - 15 q^{2} + 107 q^{4} - 15 q^{7} + 206 q^{9} - 36 q^{12} + 2 q^{14} - 54 q^{15} + 91 q^{16} + 15 q^{17} - 30 q^{19} - 12 q^{20} + 18 q^{22} + 8 q^{23} - 30 q^{24} + 86 q^{25} + 39 q^{26} - 15 q^{28} - 130 q^{30} - 24 q^{34} - 55 q^{35} - 85 q^{36} - 9 q^{37} - 60 q^{38} + 75 q^{39} - 30 q^{40} + 11 q^{42} - 12 q^{44} - 24 q^{45} - 15 q^{46} - 24 q^{48} - 5 q^{49} - 105 q^{50} + 10 q^{51} - 15 q^{52} - 16 q^{53} + 6 q^{55} + 34 q^{56} + 15 q^{59} - 204 q^{60} - 60 q^{63} - 92 q^{64} + 9 q^{66} + 45 q^{68} + 150 q^{69} - 99 q^{70} + 84 q^{71} + 45 q^{73} + 5 q^{74} - 75 q^{75} - 60 q^{77} - 70 q^{78} - 10 q^{79} - 210 q^{80} - 94 q^{81} - 120 q^{84} + 30 q^{85} + 96 q^{86} - 40 q^{88} - 54 q^{89} + 9 q^{91} - 60 q^{92} - 117 q^{93} + 5 q^{95} + 54 q^{97} + O(q^{100}) \)

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.