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Properties

Label 325.6.e
Level $325$
Weight $6$
Character orbit 325.e
Rep. character $\chi_{325}(126,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $216$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 360 228 132
Cusp forms 336 216 120
Eisenstein series 24 12 12

Trace form

\( 216 q + 5 q^{2} + 10 q^{3} - 1679 q^{4} - 124 q^{6} + 70 q^{7} - 870 q^{8} - 8232 q^{9} + O(q^{10}) \) \( 216 q + 5 q^{2} + 10 q^{3} - 1679 q^{4} - 124 q^{6} + 70 q^{7} - 870 q^{8} - 8232 q^{9} + 298 q^{11} - 2700 q^{12} + 1630 q^{13} + 1228 q^{14} - 24419 q^{16} + 1890 q^{17} - 1470 q^{18} + 1844 q^{19} - 1004 q^{21} - 1550 q^{22} - 470 q^{23} - 548 q^{24} - 10665 q^{26} - 1100 q^{27} + 5010 q^{28} + 828 q^{29} + 24576 q^{31} - 3605 q^{32} - 5680 q^{33} - 49226 q^{34} - 119141 q^{36} + 2830 q^{37} - 43420 q^{38} + 11472 q^{39} + 2274 q^{41} + 19110 q^{42} + 27330 q^{43} + 32840 q^{44} + 13956 q^{46} + 5640 q^{47} + 77760 q^{48} - 229410 q^{49} + 124192 q^{51} - 155200 q^{52} - 95620 q^{53} + 23716 q^{54} - 77766 q^{56} - 85920 q^{57} + 38295 q^{58} - 53184 q^{59} - 60684 q^{61} + 52320 q^{62} - 74180 q^{63} + 568602 q^{64} + 446672 q^{66} - 89550 q^{67} - 29135 q^{68} - 62978 q^{69} + 16782 q^{71} + 241185 q^{72} - 194540 q^{73} - 75621 q^{74} + 51492 q^{76} - 23920 q^{77} + 505050 q^{78} + 144328 q^{79} - 588712 q^{81} + 127495 q^{82} + 179320 q^{83} + 75540 q^{84} + 544940 q^{86} + 173130 q^{87} - 354730 q^{88} + 249298 q^{89} + 178194 q^{91} - 182900 q^{92} + 364240 q^{93} - 472150 q^{94} - 1061580 q^{96} - 140680 q^{97} - 577085 q^{98} + 66296 q^{99} + O(q^{100}) \)

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

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