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Properties

Label 325.6.c
Level $325$
Weight $6$
Character orbit 325.c
Rep. character $\chi_{325}(51,\cdot)$
Character field $\Q$
Dimension $108$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(210\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(325, [\chi])\).

Total New Old
Modular forms 182 114 68
Cusp forms 170 108 62
Eisenstein series 12 6 6

Trace form

\( 108 q + 20 q^{3} - 1694 q^{4} + 8044 q^{9} + O(q^{10}) \) \( 108 q + 20 q^{3} - 1694 q^{4} + 8044 q^{9} - 830 q^{12} - 150 q^{13} + 1442 q^{14} + 25526 q^{16} - 560 q^{17} + 5440 q^{22} - 800 q^{23} + 2894 q^{26} + 1220 q^{27} - 4944 q^{29} - 95868 q^{36} - 17440 q^{38} - 3812 q^{39} - 12070 q^{42} + 26040 q^{43} + 20730 q^{48} - 238716 q^{49} + 101920 q^{51} + 21020 q^{52} + 80440 q^{53} - 125974 q^{56} - 28568 q^{61} + 60540 q^{62} - 299790 q^{64} - 85120 q^{66} - 70310 q^{68} + 215076 q^{69} - 332030 q^{74} - 94100 q^{77} + 164990 q^{78} + 158732 q^{79} + 812836 q^{81} - 556860 q^{82} + 434820 q^{87} - 535820 q^{88} - 490456 q^{91} - 191000 q^{92} - 151662 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(325, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 2}\)