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Properties

Label 1001.2.ck
Level $1001$
Weight $2$
Character orbit 1001.ck
Rep. character $\chi_{1001}(122,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.ck (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 464 368 96
Cusp forms 432 368 64
Eisenstein series 32 0 32

Trace form

\( 368 q + 4 q^{7} + 176 q^{9} + O(q^{10}) \) \( 368 q + 4 q^{7} + 176 q^{9} - 32 q^{14} + 32 q^{15} + 160 q^{16} + 16 q^{18} - 12 q^{19} + 16 q^{21} - 60 q^{26} + 20 q^{28} - 16 q^{29} - 60 q^{31} + 20 q^{32} - 48 q^{35} - 12 q^{39} + 240 q^{40} - 76 q^{42} - 8 q^{44} - 36 q^{46} - 72 q^{47} - 168 q^{50} - 132 q^{52} + 8 q^{53} - 72 q^{54} - 120 q^{57} - 40 q^{58} + 48 q^{59} - 16 q^{60} - 52 q^{63} + 28 q^{65} - 60 q^{66} - 36 q^{67} - 44 q^{70} - 32 q^{71} - 104 q^{72} - 180 q^{73} - 48 q^{74} + 264 q^{78} - 8 q^{79} - 288 q^{80} - 184 q^{81} + 260 q^{84} + 176 q^{85} - 80 q^{86} + 144 q^{87} + 48 q^{89} - 44 q^{91} - 232 q^{92} + 8 q^{93} + 120 q^{96} + 92 q^{98} + O(q^{100}) \)

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

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