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Properties

Label 1300.2.bk
Level $1300$
Weight $2$
Character orbit 1300.bk
Rep. character $\chi_{1300}(799,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $488$
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.bk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
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 888 520 368
Cusp forms 792 488 304
Eisenstein series 96 32 64

Trace form

\( 488 q + 12 q^{4} - 16 q^{6} - 220 q^{9} + O(q^{10}) \) \( 488 q + 12 q^{4} - 16 q^{6} - 220 q^{9} + 48 q^{14} + 12 q^{16} - 40 q^{21} + 84 q^{24} - 40 q^{26} + 8 q^{29} + 48 q^{34} - 48 q^{36} + 8 q^{41} + 8 q^{44} - 80 q^{46} + 24 q^{49} - 104 q^{54} - 120 q^{56} + 12 q^{61} - 72 q^{66} + 24 q^{69} + 4 q^{74} + 60 q^{76} - 164 q^{81} + 88 q^{84} + 72 q^{86} + 36 q^{89} + 36 q^{94} + 196 q^{96} + O(q^{100}) \)

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

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