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Properties

Label 1001.2.cf
Level $1001$
Weight $2$
Character orbit 1001.cf
Rep. character $\chi_{1001}(109,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $432$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 1001 = 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1001.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1001 \)
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 464 464 0
Cusp forms 432 432 0
Eisenstein series 32 32 0

Trace form

\( 432 q - 8 q^{3} - 4 q^{5} - 208 q^{9} + O(q^{10}) \) \( 432 q - 8 q^{3} - 4 q^{5} - 208 q^{9} - 2 q^{11} - 40 q^{14} + 24 q^{15} + 184 q^{16} - 16 q^{20} - 24 q^{22} - 4 q^{26} + 16 q^{27} - 4 q^{31} + 8 q^{33} - 112 q^{34} + 8 q^{37} - 60 q^{42} - 18 q^{44} + 64 q^{45} - 28 q^{47} + 32 q^{48} + 48 q^{53} - 24 q^{55} - 20 q^{58} - 4 q^{59} - 56 q^{60} - 48 q^{66} - 4 q^{67} + 80 q^{70} + 8 q^{71} + 56 q^{78} + 20 q^{80} - 264 q^{81} - 44 q^{86} - 72 q^{89} - 36 q^{91} - 136 q^{92} + 4 q^{93} + 80 q^{99} + O(q^{100}) \)

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.