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Properties

Label 1001.2.di
Level $1001$
Weight $2$
Character orbit 1001.di
Rep. character $\chi_{1001}(25,\cdot)$
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.di (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

\( 864 q - 6 q^{3} - 110 q^{4} + 82 q^{9} + O(q^{10}) \) \( 864 q - 6 q^{3} - 110 q^{4} + 82 q^{9} + 32 q^{10} - 48 q^{12} - 12 q^{13} - 4 q^{14} + 74 q^{16} - 16 q^{17} - 124 q^{22} - 16 q^{23} - 98 q^{25} + 9 q^{26} - 48 q^{27} + 4 q^{29} + 2 q^{30} + 6 q^{35} + 256 q^{36} - 4 q^{38} + 21 q^{39} + 38 q^{40} - 142 q^{42} - 64 q^{43} - 40 q^{48} + 48 q^{49} - 74 q^{51} + q^{52} - 38 q^{53} - 32 q^{55} - 204 q^{56} + 54 q^{61} + 32 q^{62} - 48 q^{64} + 26 q^{65} - 38 q^{66} + 4 q^{68} + 124 q^{69} + 18 q^{74} - 22 q^{75} + 26 q^{77} - 60 q^{78} - 22 q^{79} + 102 q^{81} + 2 q^{82} - 196 q^{87} + 40 q^{88} + 60 q^{90} + 28 q^{91} + 20 q^{92} + 2 q^{95} + O(q^{100}) \)

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.