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Properties

Label 1300.2.ci
Level $1300$
Weight $2$
Character orbit 1300.ci
Rep. character $\chi_{1300}(31,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1648$
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.ci (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1300 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 1712 1712 0
Cusp forms 1648 1648 0
Eisenstein series 64 64 0

Trace form

\( 1648 q - 6 q^{2} - 14 q^{5} - 14 q^{6} - 6 q^{8} + 372 q^{9} + O(q^{10}) \) \( 1648 q - 6 q^{2} - 14 q^{5} - 14 q^{6} - 6 q^{8} + 372 q^{9} - 12 q^{13} - 12 q^{14} - 36 q^{16} - 20 q^{18} - 6 q^{20} + 24 q^{21} + 32 q^{22} - 28 q^{24} - 16 q^{26} - 30 q^{28} - 24 q^{29} - 36 q^{32} - 36 q^{33} - 14 q^{34} - 42 q^{37} - 48 q^{40} - 32 q^{41} - 36 q^{42} + 10 q^{44} - 18 q^{45} + 42 q^{46} - 36 q^{48} - 48 q^{50} + 32 q^{52} - 12 q^{53} - 50 q^{54} - 88 q^{57} + 74 q^{58} + 2 q^{60} - 64 q^{61} - 26 q^{65} - 20 q^{66} - 168 q^{68} - 80 q^{70} + 44 q^{72} + 40 q^{73} - 32 q^{74} + 20 q^{76} - 112 q^{78} + 172 q^{80} - 420 q^{81} - 74 q^{85} - 18 q^{86} + 66 q^{89} + 20 q^{92} - 56 q^{93} + 84 q^{94} - 48 q^{96} + 8 q^{97} + 208 q^{98} + O(q^{100}) \)

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.