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Properties

Label 325.6.bf
Level $325$
Weight $6$
Character orbit 325.bf
Rep. character $\chi_{325}(9,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1392$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.bf (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 1424 1424 0
Cusp forms 1392 1392 0
Eisenstein series 32 32 0

Trace form

\( 1392 q - 5 q^{2} - 5 q^{3} - 2787 q^{4} - 114 q^{5} + 125 q^{6} - 20 q^{8} - 14097 q^{9} + O(q^{10}) \) \( 1392 q - 5 q^{2} - 5 q^{3} - 2787 q^{4} - 114 q^{5} + 125 q^{6} - 20 q^{8} - 14097 q^{9} - 152 q^{10} - 3 q^{11} - 20 q^{12} - 10 q^{13} + 2932 q^{14} - 2001 q^{15} + 48305 q^{16} - 5 q^{17} - 5271 q^{19} + 5866 q^{20} - 1470 q^{21} - 730 q^{22} + 4605 q^{23} - 4654 q^{24} + 15302 q^{25} + 14004 q^{26} - 20 q^{27} - 10245 q^{28} - 6451 q^{29} + 4411 q^{30} - 12 q^{31} - 45865 q^{33} + 32756 q^{34} + 18570 q^{35} + 226199 q^{36} + 19980 q^{37} - 20 q^{38} - 17248 q^{39} - 3880 q^{40} - 13066 q^{41} - 77765 q^{42} - 3980 q^{44} + 125074 q^{45} + 14305 q^{46} - 51070 q^{47} - 140150 q^{48} + 1632672 q^{49} - 67119 q^{50} + 386664 q^{51} + 189245 q^{52} - 163270 q^{53} - 49999 q^{54} + 3656 q^{55} + 135760 q^{56} + 191455 q^{58} - 1917 q^{59} - 157964 q^{60} + 103859 q^{61} + 75905 q^{62} - 168420 q^{63} + 1669892 q^{64} + 547 q^{65} - 336304 q^{66} - 5 q^{67} - 44394 q^{69} + 386250 q^{70} + 5453 q^{71} + 7545 q^{72} + 332940 q^{73} + 375784 q^{74} - 89372 q^{75} - 279946 q^{76} - 363010 q^{77} + 542450 q^{78} + 277956 q^{79} + 622987 q^{80} + 880297 q^{81} - 470350 q^{83} - 35838 q^{84} - 68846 q^{85} - 201900 q^{86} - 27795 q^{87} + 350175 q^{88} - 448698 q^{89} - 89422 q^{90} - 134929 q^{91} - 466160 q^{92} - 175539 q^{94} - 328625 q^{95} + 9094 q^{96} - 5 q^{97} + 1594130 q^{98} + 160704 q^{99} + O(q^{100}) \)

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.