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Properties

Label 1001.2.cz
Level $1001$
Weight $2$
Character orbit 1001.cz
Rep. character $\chi_{1001}(17,\cdot)$
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.cz (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

\( 864 q - 9 q^{3} - 214 q^{4} - 15 q^{7} - 103 q^{9} + O(q^{10}) \) \( 864 q - 9 q^{3} - 214 q^{4} - 15 q^{7} - 103 q^{9} - 18 q^{11} - 36 q^{12} + 2 q^{14} - 54 q^{15} - 182 q^{16} - 15 q^{19} + 12 q^{20} + 18 q^{22} - 16 q^{23} - 15 q^{24} + 86 q^{25} + 15 q^{26} - 15 q^{28} + 65 q^{30} + 24 q^{34} + 20 q^{35} - 85 q^{36} - 60 q^{38} - 45 q^{39} - 30 q^{40} + 53 q^{42} + 12 q^{44} - 48 q^{45} + 24 q^{48} - 17 q^{49} - 105 q^{50} + 10 q^{51} - 15 q^{52} - 16 q^{53} - 6 q^{55} - 170 q^{56} - 45 q^{58} + 30 q^{59} + 204 q^{60} - 15 q^{61} + 105 q^{63} - 92 q^{64} + 9 q^{66} - 150 q^{69} + 99 q^{70} + 84 q^{71} + 255 q^{72} - 45 q^{73} - 10 q^{74} - 60 q^{77} - 70 q^{78} - 10 q^{79} - 105 q^{80} + 47 q^{81} - 9 q^{82} + 45 q^{84} + 30 q^{85} - 96 q^{86} + 20 q^{88} - 108 q^{89} - 117 q^{91} - 60 q^{92} + 165 q^{94} - 10 q^{95} - 54 q^{97} + O(q^{100}) \)

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.