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Properties

Label 1300.2.cq
Level $1300$
Weight $2$
Character orbit 1300.cq
Rep. character $\chi_{1300}(11,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $3296$
Sturm bound $420$

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Defining parameters

Level: \( N \) \(=\) \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1300.cq (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1300 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(420\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1300, [\chi])\).

Total New Old
Modular forms 3424 3424 0
Cusp forms 3296 3296 0
Eisenstein series 128 128 0

Trace form

\( 3296 q - 12 q^{2} - 18 q^{4} - 34 q^{5} - 4 q^{6} - 12 q^{8} - 408 q^{9} + O(q^{10}) \) \( 3296 q - 12 q^{2} - 18 q^{4} - 34 q^{5} - 4 q^{6} - 12 q^{8} - 408 q^{9} - 24 q^{10} - 24 q^{13} - 24 q^{14} + 18 q^{16} - 36 q^{17} - 28 q^{18} - 18 q^{20} - 60 q^{21} + 40 q^{22} - 20 q^{24} - 32 q^{26} + 12 q^{28} - 12 q^{29} - 24 q^{30} - 72 q^{32} - 4 q^{34} + 18 q^{36} + 6 q^{37} + 24 q^{40} - 64 q^{41} - 18 q^{42} - 28 q^{44} - 60 q^{45} + 60 q^{46} + 18 q^{48} - 96 q^{49} - 204 q^{50} - 50 q^{52} - 60 q^{53} + 8 q^{54} + 90 q^{56} - 8 q^{57} - 92 q^{58} + 4 q^{60} - 32 q^{61} - 18 q^{62} - 52 q^{65} + 32 q^{66} - 36 q^{68} - 36 q^{69} + 14 q^{70} - 62 q^{72} - 76 q^{73} - 16 q^{74} - 68 q^{76} - 134 q^{78} + 260 q^{80} + 312 q^{81} - 48 q^{82} - 144 q^{84} + 32 q^{85} + 198 q^{88} - 102 q^{89} - 56 q^{92} - 40 q^{93} - 102 q^{94} + 30 q^{96} - 44 q^{97} - 100 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1300, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.