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Properties

Label 325.6.o
Level $325$
Weight $6$
Character orbit 325.o
Rep. character $\chi_{325}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $204$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 364 212 152
Cusp forms 340 204 136
Eisenstein series 24 8 16

Trace form

\( 204 q + 1570 q^{4} + 126 q^{6} + 7396 q^{9} + O(q^{10}) \) \( 204 q + 1570 q^{4} + 126 q^{6} + 7396 q^{9} + 778 q^{11} + 3736 q^{14} - 26418 q^{16} + 5704 q^{19} + 2744 q^{21} - 11624 q^{24} + 21136 q^{26} - 3726 q^{29} - 128 q^{31} + 27000 q^{34} - 108984 q^{36} - 38980 q^{39} - 4260 q^{41} + 34424 q^{44} - 30494 q^{46} + 232574 q^{49} + 215248 q^{51} - 148634 q^{54} - 7810 q^{56} + 102048 q^{59} + 159610 q^{61} - 818600 q^{64} - 139692 q^{66} - 10068 q^{69} + 58994 q^{71} - 328582 q^{74} - 508388 q^{76} + 423656 q^{79} + 50074 q^{81} - 242860 q^{84} + 41664 q^{86} + 246712 q^{89} - 358422 q^{91} - 358206 q^{94} - 1604772 q^{96} + 106320 q^{99} + O(q^{100}) \)

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

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