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Properties

Label 1300.2.cm
Level $1300$
Weight $2$
Character orbit 1300.cm
Rep. character $\chi_{1300}(9,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $272$
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.cm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(420\)

Dimensions

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

Total New Old
Modular forms 1728 272 1456
Cusp forms 1632 272 1360
Eisenstein series 96 0 96

Trace form

\( 272 q - 30 q^{9} + O(q^{10}) \) \( 272 q - 30 q^{9} + 30 q^{15} + 12 q^{19} + 10 q^{23} - 24 q^{25} + 22 q^{29} - 60 q^{33} + 6 q^{35} - 10 q^{37} + 8 q^{39} + 5 q^{41} + 48 q^{45} - 50 q^{47} + 104 q^{49} - 20 q^{51} - 20 q^{53} + 15 q^{55} + 6 q^{59} - 12 q^{61} - 5 q^{63} + 65 q^{65} - q^{69} + 16 q^{71} - 160 q^{73} + 83 q^{75} - 120 q^{77} + 8 q^{79} + 22 q^{81} + 70 q^{83} + 6 q^{85} + 70 q^{87} - 3 q^{89} + 26 q^{91} - 10 q^{95} + 40 q^{99} + O(q^{100}) \)

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

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