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Properties

Label 1001.2.dg
Level $1001$
Weight $2$
Character orbit 1001.dg
Rep. character $\chi_{1001}(139,\cdot)$
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.dg (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

\( 864 q - 10 q^{2} - 110 q^{4} - 5 q^{7} - 40 q^{8} - 100 q^{9} + O(q^{10}) \) \( 864 q - 10 q^{2} - 110 q^{4} - 5 q^{7} - 40 q^{8} - 100 q^{9} + 24 q^{14} - 12 q^{15} + 74 q^{16} - 40 q^{18} + 52 q^{22} - 16 q^{23} + 160 q^{25} - 5 q^{28} - 30 q^{29} + 50 q^{30} + 20 q^{35} + 56 q^{36} + 18 q^{37} - 60 q^{39} - 13 q^{42} + 16 q^{44} + 30 q^{46} + 11 q^{49} - 60 q^{50} + 120 q^{51} + 16 q^{53} - 110 q^{56} - 40 q^{57} - 2 q^{58} + 120 q^{60} + 20 q^{63} - 72 q^{64} - 152 q^{67} - 50 q^{70} - 26 q^{71} - 70 q^{72} - 10 q^{74} - 56 q^{77} - 12 q^{78} - 40 q^{79} + 128 q^{81} + 170 q^{84} - 30 q^{85} + 72 q^{86} + 28 q^{88} + 31 q^{91} + 80 q^{92} - 74 q^{93} - 10 q^{95} - 12 q^{99} + O(q^{100}) \)

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.