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Properties

Label 1300.2.p
Level $1300$
Weight $2$
Character orbit 1300.p
Rep. character $\chi_{1300}(207,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $244$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 260 \)
Character field: \(\Q(i)\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 444 260 184
Cusp forms 396 244 152
Eisenstein series 48 16 32

Trace form

\( 244 q + O(q^{10}) \) \( 244 q + 24 q^{12} + 6 q^{13} - 40 q^{16} + 28 q^{17} + 24 q^{22} - 52 q^{26} + 88 q^{36} - 4 q^{38} - 8 q^{42} + 44 q^{48} - 44 q^{52} + 12 q^{53} - 40 q^{56} - 16 q^{61} + 28 q^{62} - 120 q^{66} + 40 q^{68} + 64 q^{77} + 20 q^{78} - 196 q^{81} - 52 q^{82} + 116 q^{88} + 4 q^{92} + O(q^{100}) \)

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

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