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Properties

Label 325.6.bn
Level $325$
Weight $6$
Character orbit 325.bn
Rep. character $\chi_{325}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2768$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.bn (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 2832 2832 0
Cusp forms 2768 2768 0
Eisenstein series 64 64 0

Trace form

\( 2768 q - 26 q^{2} - 8 q^{3} + 5442 q^{4} - 114 q^{5} - 12 q^{6} - 24 q^{7} + 628 q^{8} - 10 q^{9} + O(q^{10}) \) \( 2768 q - 26 q^{2} - 8 q^{3} + 5442 q^{4} - 114 q^{5} - 12 q^{6} - 24 q^{7} + 628 q^{8} - 10 q^{9} + 40 q^{10} - 12 q^{11} + 1456 q^{12} - 2242 q^{13} - 40 q^{14} + 568 q^{15} + 85498 q^{16} - 2680 q^{17} + 8760 q^{19} + 10846 q^{20} - 2442 q^{21} + 3074 q^{22} + 7092 q^{23} + 1816 q^{24} - 542 q^{25} - 32 q^{26} - 9164 q^{27} - 10446 q^{28} - 14190 q^{29} - 6824 q^{30} - 12 q^{31} + 72046 q^{32} - 24732 q^{33} + 42052 q^{34} - 59900 q^{35} + 302 q^{36} + 141638 q^{37} - 128 q^{38} - 7180 q^{39} + 27576 q^{40} + 25178 q^{41} + 15526 q^{42} + 12312 q^{43} - 148 q^{44} - 98252 q^{45} - 12 q^{46} + 51030 q^{47} - 146178 q^{48} + 3092488 q^{49} + 387156 q^{50} + 36904 q^{52} + 14210 q^{53} + 68938 q^{54} + 83774 q^{55} + 155764 q^{56} - 232108 q^{57} - 694550 q^{58} - 20 q^{59} + 199872 q^{60} - 6 q^{61} + 137410 q^{62} + 592652 q^{63} - 2604672 q^{64} + 368702 q^{65} - 24 q^{66} + 72038 q^{67} + 320182 q^{68} + 44280 q^{69} + 161358 q^{70} - 12 q^{71} - 165324 q^{72} - 50852 q^{73} - 11400 q^{74} + 55774 q^{75} - 4128 q^{76} - 280488 q^{77} + 383428 q^{78} - 40 q^{79} - 494336 q^{80} + 725880 q^{81} - 1364552 q^{82} - 470350 q^{83} - 100018 q^{84} + 18936 q^{85} - 332 q^{86} + 427848 q^{87} - 2349400 q^{88} - 505420 q^{89} + 8616 q^{90} + 81638 q^{91} - 746272 q^{92} - 100878 q^{93} - 386154 q^{94} + 36456 q^{95} - 518442 q^{96} - 567198 q^{97} - 1262564 q^{98} - 972 q^{99} + O(q^{100}) \)

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.