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Properties

Label 1300.2.cd
Level $1300$
Weight $2$
Character orbit 1300.cd
Rep. character $\chi_{1300}(27,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1440$
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.cd (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 100 \)
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 1440 272
Cusp forms 1648 1440 208
Eisenstein series 64 0 64

Trace form

\( 1440 q + 12 q^{8} + O(q^{10}) \) \( 1440 q + 12 q^{8} + 8 q^{10} + 8 q^{12} - 28 q^{18} + 8 q^{22} + 20 q^{28} + 32 q^{30} + 40 q^{32} - 16 q^{33} - 48 q^{38} + 8 q^{40} - 160 q^{42} - 140 q^{44} - 60 q^{48} - 40 q^{50} - 8 q^{52} + 48 q^{53} - 80 q^{58} - 220 q^{60} - 60 q^{62} - 60 q^{64} + 16 q^{68} + 60 q^{70} - 40 q^{72} + 16 q^{73} - 48 q^{77} + 20 q^{80} + 360 q^{81} + 52 q^{82} + 160 q^{84} - 48 q^{85} - 12 q^{88} + 256 q^{90} + 236 q^{92} - 176 q^{93} + 160 q^{94} - 40 q^{96} - 320 q^{97} + 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)