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Properties

Label 325.6.bi
Level $325$
Weight $6$
Character orbit 325.bi
Rep. character $\chi_{325}(28,\cdot)$
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.bi (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

\( 2768 q - 14 q^{2} - 8 q^{3} - 5502 q^{4} - 12 q^{6} - 8 q^{7} - 20 q^{8} - 10 q^{9} + O(q^{10}) \) \( 2768 q - 14 q^{2} - 8 q^{3} - 5502 q^{4} - 12 q^{6} - 8 q^{7} - 20 q^{8} - 10 q^{9} - 88 q^{10} - 12 q^{11} - 1456 q^{12} - 1876 q^{13} - 40 q^{14} - 600 q^{15} + 85498 q^{16} - 4094 q^{17} - 31340 q^{18} + 8760 q^{19} - 4770 q^{20} + 2418 q^{21} + 3074 q^{22} - 7140 q^{23} - 1816 q^{24} + 542 q^{25} - 32 q^{26} - 9164 q^{27} + 6062 q^{28} - 14190 q^{29} + 6776 q^{30} - 12 q^{31} + 32202 q^{32} + 61092 q^{33} + 5708 q^{34} + 90100 q^{35} - 338 q^{36} - 77376 q^{37} + 128 q^{38} - 7180 q^{39} + 27576 q^{40} - 67102 q^{41} - 69410 q^{42} - 12360 q^{43} + 108 q^{44} + 165240 q^{45} - 12 q^{46} - 58230 q^{47} + 97626 q^{48} - 3092488 q^{49} + 356144 q^{50} + 185160 q^{52} + 14210 q^{53} + 63362 q^{54} - 149650 q^{55} - 180376 q^{56} + 713310 q^{58} - 20 q^{59} + 223632 q^{60} - 6 q^{61} + 86894 q^{62} + 709676 q^{63} + 2604672 q^{64} + 163254 q^{65} - 24 q^{66} + 271642 q^{67} - 2282 q^{68} + 44280 q^{69} + 13022 q^{70} - 12 q^{71} - 54404 q^{72} - 332980 q^{73} + 11400 q^{74} - 473362 q^{75} - 4128 q^{76} + 280488 q^{77} - 1259468 q^{78} - 40 q^{79} + 483632 q^{80} - 4846200 q^{81} - 334336 q^{82} - 196638 q^{83} + 99978 q^{84} + 559946 q^{85} + 308 q^{86} - 462936 q^{87} - 3156632 q^{88} - 658570 q^{89} - 8616 q^{90} - 81662 q^{91} - 746272 q^{92} + 260478 q^{93} - 385386 q^{94} - 36504 q^{95} + 468498 q^{96} + 511474 q^{97} - 1530520 q^{98} + 972 q^{99} + O(q^{100}) \)

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.