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Properties

Label 1300.2.db
Level $1300$
Weight $2$
Character orbit 1300.db
Rep. character $\chi_{1300}(19,\cdot)$
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.db (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

\( 3296 q - 20 q^{2} - 18 q^{4} - 30 q^{5} - 20 q^{6} - 20 q^{8} + 384 q^{9} + O(q^{10}) \) \( 3296 q - 20 q^{2} - 18 q^{4} - 30 q^{5} - 20 q^{6} - 20 q^{8} + 384 q^{9} - 24 q^{10} - 40 q^{13} - 24 q^{14} - 30 q^{16} - 60 q^{17} - 18 q^{20} + 12 q^{21} - 60 q^{22} - 44 q^{24} - 32 q^{26} - 60 q^{28} - 12 q^{29} - 24 q^{30} - 40 q^{33} - 20 q^{34} - 54 q^{36} - 90 q^{37} + 24 q^{40} + 16 q^{41} - 10 q^{42} - 28 q^{44} - 84 q^{45} - 84 q^{46} - 10 q^{48} - 96 q^{49} - 136 q^{50} - 110 q^{52} - 60 q^{53} + 76 q^{54} - 126 q^{56} + 100 q^{58} + 28 q^{60} + 8 q^{61} - 30 q^{62} - 52 q^{65} - 80 q^{66} - 36 q^{69} - 10 q^{70} - 50 q^{72} - 40 q^{73} - 16 q^{74} - 28 q^{76} - 50 q^{78} - 348 q^{80} + 360 q^{81} - 16 q^{85} - 24 q^{86} + 330 q^{88} - 102 q^{89} - 40 q^{92} - 102 q^{94} - 54 q^{96} - 40 q^{97} - 320 q^{98} + O(q^{100}) \)

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.