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Properties

Label 1001.2.ci
Level $1001$
Weight $2$
Character orbit 1001.ci
Rep. character $\chi_{1001}(45,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $376$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.ci (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 464 376 88
Cusp forms 432 376 56
Eisenstein series 32 0 32

Trace form

\( 376 q + 4 q^{7} + 192 q^{9} + O(q^{10}) \) \( 376 q + 4 q^{7} + 192 q^{9} + 16 q^{12} + 16 q^{14} - 16 q^{15} - 400 q^{16} - 32 q^{18} - 16 q^{19} - 24 q^{21} - 60 q^{26} - 20 q^{28} + 8 q^{29} + 48 q^{30} - 4 q^{31} - 40 q^{32} + 24 q^{35} + 40 q^{37} - 20 q^{39} - 120 q^{40} - 4 q^{42} - 120 q^{43} + 16 q^{44} - 36 q^{46} + 88 q^{49} - 72 q^{50} - 48 q^{51} + 88 q^{52} + 8 q^{53} + 72 q^{54} - 28 q^{57} + 32 q^{58} - 48 q^{59} + 56 q^{60} - 16 q^{63} + 28 q^{65} - 60 q^{66} + 16 q^{67} + 84 q^{69} + 208 q^{70} + 16 q^{71} - 104 q^{72} - 92 q^{73} - 48 q^{74} + 56 q^{75} + 152 q^{76} + 144 q^{78} - 8 q^{79} - 72 q^{80} - 188 q^{81} + 48 q^{82} - 132 q^{83} - 184 q^{84} + 8 q^{85} - 32 q^{86} - 72 q^{88} + 48 q^{89} + 48 q^{91} + 272 q^{92} - 20 q^{93} + 4 q^{97} + 32 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1001, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1001, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)