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Properties

Label 1001.2.dl
Level $1001$
Weight $2$
Character orbit 1001.dl
Rep. character $\chi_{1001}(61,\cdot)$
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.dl (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

\( 864 q + 5 q^{2} - 101 q^{4} - 18 q^{5} - 5 q^{7} - 40 q^{8} + 182 q^{9} + O(q^{10}) \) \( 864 q + 5 q^{2} - 101 q^{4} - 18 q^{5} - 5 q^{7} - 40 q^{8} + 182 q^{9} - 12 q^{11} - 60 q^{12} - 18 q^{14} + 6 q^{15} + 107 q^{16} - 45 q^{17} - 10 q^{18} - 72 q^{20} - 38 q^{22} + 8 q^{23} - 98 q^{25} - 57 q^{26} - 5 q^{28} - 130 q^{30} - 18 q^{31} - 55 q^{35} + 119 q^{36} - 9 q^{37} + 24 q^{38} + 75 q^{39} - 30 q^{40} - 180 q^{41} - 37 q^{42} - 8 q^{44} - 60 q^{45} + 45 q^{46} - 18 q^{47} + 24 q^{48} - q^{49} + 15 q^{50} - 30 q^{51} - 15 q^{52} + 4 q^{53} + 36 q^{55} - 170 q^{56} - 40 q^{57} + 34 q^{58} - 33 q^{59} - 30 q^{60} - 100 q^{63} + 204 q^{64} - 75 q^{66} - 128 q^{67} + 105 q^{68} - 42 q^{69} - 89 q^{70} + 16 q^{71} - 70 q^{72} + 15 q^{73} + 5 q^{74} + 177 q^{75} + 4 q^{77} - 102 q^{78} - 10 q^{79} - 94 q^{81} + 110 q^{84} - 30 q^{85} + 6 q^{86} + 40 q^{88} + 6 q^{89} - 53 q^{91} - 76 q^{92} + 31 q^{93} + 5 q^{95} - 270 q^{96} + 102 q^{97} - 36 q^{99} + O(q^{100}) \)

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.