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Properties

Label 1001.2.de
Level $1001$
Weight $2$
Character orbit 1001.de
Rep. character $\chi_{1001}(40,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.de (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 928 768 160
Cusp forms 864 768 96
Eisenstein series 64 0 64

Trace form

\( 768 q - 92 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 96 q^{9} + O(q^{10}) \) \( 768 q - 92 q^{4} + 12 q^{5} - 10 q^{7} - 40 q^{8} - 96 q^{9} + 2 q^{11} + 4 q^{14} + 24 q^{15} + 128 q^{16} - 30 q^{17} - 50 q^{18} + 36 q^{22} - 36 q^{23} - 100 q^{25} + 60 q^{28} + 20 q^{29} - 36 q^{31} + 36 q^{33} - 80 q^{35} - 132 q^{36} - 16 q^{37} - 42 q^{38} - 180 q^{40} - 150 q^{42} - 116 q^{44} + 156 q^{45} + 70 q^{46} - 24 q^{47} - 38 q^{49} - 20 q^{51} + 16 q^{53} - 28 q^{56} - 160 q^{57} - 82 q^{58} - 60 q^{59} - 108 q^{60} + 30 q^{61} + 10 q^{63} + 120 q^{64} + 264 q^{66} - 24 q^{67} + 90 q^{68} + 40 q^{70} - 24 q^{71} + 50 q^{72} - 100 q^{74} + 72 q^{75} + 70 q^{77} - 80 q^{78} + 130 q^{79} + 180 q^{80} + 120 q^{81} + 216 q^{82} - 120 q^{84} - 140 q^{85} + 118 q^{86} - 46 q^{88} + 16 q^{91} - 40 q^{92} + 122 q^{93} + 30 q^{94} - 70 q^{95} - 420 q^{96} + 72 q^{99} + O(q^{100}) \)

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

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