Properties

Label 1300.2.be
Level $1300$
Weight $2$
Character orbit 1300.be
Rep. character $\chi_{1300}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $136$
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.be (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 864 136 728
Cusp forms 816 136 680
Eisenstein series 48 0 48

Trace form

\( 136 q - 30 q^{9} + O(q^{10}) \) \( 136 q - 30 q^{9} + 22 q^{23} - 14 q^{25} - 12 q^{27} - 2 q^{29} + 2 q^{39} - 12 q^{43} - 104 q^{49} + 24 q^{51} - 38 q^{53} + 18 q^{55} + 12 q^{61} - 19 q^{65} - 66 q^{69} + 110 q^{75} + 36 q^{77} + 4 q^{79} - 26 q^{81} + 46 q^{87} - 4 q^{91} - 10 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)