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Properties

Label 1300.2.bv
Level $1300$
Weight $2$
Character orbit 1300.bv
Rep. character $\chi_{1300}(851,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $508$
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.bv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 888 556 332
Cusp forms 792 508 284
Eisenstein series 96 48 48

Trace form

\( 508 q + 4 q^{2} + 6 q^{4} - 14 q^{6} + 10 q^{8} + 234 q^{9} + O(q^{10}) \) \( 508 q + 4 q^{2} + 6 q^{4} - 14 q^{6} + 10 q^{8} + 234 q^{9} + 8 q^{13} - 8 q^{14} - 14 q^{16} + 12 q^{17} + 18 q^{18} - 20 q^{21} - 58 q^{24} - 14 q^{26} + 4 q^{28} + 4 q^{29} + 4 q^{32} + 20 q^{33} - 22 q^{34} + 18 q^{36} + 6 q^{37} - 52 q^{41} - 36 q^{42} - 32 q^{44} + 18 q^{46} + 18 q^{48} + 84 q^{49} + 4 q^{52} + 36 q^{53} - 48 q^{54} + 36 q^{56} + 84 q^{57} - 26 q^{58} - 14 q^{61} - 6 q^{62} + 96 q^{66} + 4 q^{68} + 12 q^{69} + 56 q^{72} + 6 q^{73} + 18 q^{74} + 42 q^{76} - 16 q^{78} - 182 q^{81} + 66 q^{82} - 108 q^{84} + 72 q^{86} - 96 q^{88} + 42 q^{89} - 28 q^{92} - 52 q^{93} + 62 q^{94} + 68 q^{96} - 42 q^{97} - 76 q^{98} + O(q^{100}) \)

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.

Decomposition of \(S_{2}^{\mathrm{old}}(1300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)