↑

Properties

Label 325.6.y
Level $325$
Weight $6$
Character orbit 325.y
Rep. character $\chi_{325}(16,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $1376$
Sturm bound $210$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.y (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 1408 1408 0
Cusp forms 1376 1376 0
Eisenstein series 32 32 0

Trace form

\( 1376 q + 5 q^{2} - 3 q^{3} + 2685 q^{4} - 131 q^{6} - 8 q^{7} - 908 q^{8} + 13281 q^{9} + O(q^{10}) \) \( 1376 q + 5 q^{2} - 3 q^{3} + 2685 q^{4} - 131 q^{6} - 8 q^{7} - 908 q^{8} + 13281 q^{9} - 108 q^{10} - 3 q^{11} - 2696 q^{12} + 1854 q^{13} + 3316 q^{14} + 1993 q^{15} + 37193 q^{16} + 1825 q^{17} + 29332 q^{18} - 5271 q^{19} - 2134 q^{20} + 1446 q^{21} + 3096 q^{22} - 2509 q^{23} - 3554 q^{24} - 4428 q^{25} - 17836 q^{26} + 9120 q^{27} + 6205 q^{28} - 9401 q^{29} + 3871 q^{30} - 12 q^{31} - 68222 q^{32} + 28101 q^{33} - 4100 q^{34} + 3256 q^{35} + 188099 q^{36} - 35769 q^{37} + 32596 q^{38} - 18220 q^{39} - 154752 q^{40} - 7890 q^{41} + 87871 q^{42} + 11016 q^{43} - 4236 q^{44} - 123007 q^{45} - 14311 q^{46} + 58206 q^{47} - 42118 q^{48} - 1459816 q^{49} - 100735 q^{50} - 386728 q^{51} - 156233 q^{52} + 164440 q^{53} - 51329 q^{54} - 9832 q^{55} - 131670 q^{56} - 234052 q^{57} - 91063 q^{58} - 1917 q^{59} - 86404 q^{60} - 122815 q^{61} - 118211 q^{62} + 154052 q^{63} - 934780 q^{64} + 52849 q^{65} + 274072 q^{66} - 164811 q^{67} - 64806 q^{68} - 46338 q^{69} + 237658 q^{70} - 5459 q^{71} + 125807 q^{72} - 450404 q^{73} + 379328 q^{74} + 347282 q^{75} + 271738 q^{76} - 154554 q^{77} + 335188 q^{78} + 277956 q^{79} - 259405 q^{80} + 1179851 q^{81} + 1309240 q^{82} - 367782 q^{83} - 138880 q^{84} - 616281 q^{85} + 201876 q^{86} + 91067 q^{87} + 22937 q^{88} - 295548 q^{89} - 600430 q^{90} + 134917 q^{91} + 267060 q^{92} + 326742 q^{93} - 175411 q^{94} + 670443 q^{95} - 59038 q^{96} - 277867 q^{97} + 490358 q^{98} + 158760 q^{99} + O(q^{100}) \)

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.