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Properties

Label 1300.2.bo
Level $1300$
Weight $2$
Character orbit 1300.bo
Rep. character $\chi_{1300}(43,\cdot)$
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.bo (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

\( 488 q + 6 q^{2} - 12 q^{6} + O(q^{10}) \) \( 488 q + 6 q^{2} - 12 q^{6} + 12 q^{12} + 6 q^{13} - 20 q^{16} + 14 q^{17} + 12 q^{22} + 40 q^{26} + 6 q^{28} + 36 q^{32} + 12 q^{33} - 4 q^{36} - 18 q^{37} + 16 q^{38} - 24 q^{41} - 40 q^{42} - 12 q^{46} + 40 q^{48} + 50 q^{52} + 12 q^{53} + 28 q^{56} - 66 q^{58} - 8 q^{61} + 44 q^{62} - 96 q^{66} + 44 q^{68} + 54 q^{72} - 12 q^{76} - 40 q^{77} + 100 q^{78} + 172 q^{81} + 58 q^{82} + 10 q^{88} - 100 q^{92} + 48 q^{93} + 12 q^{97} + 162 q^{98} + O(q^{100}) \)

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

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