↑

Properties

Label 325.6.bh
Level $325$
Weight $6$
Character orbit 325.bh
Rep. character $\chi_{325}(4,\cdot)$
Character field $\Q(\zeta_{30})$
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.bh (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 1408 1408 0
Cusp forms 1376 1376 0
Eisenstein series 32 32 0

Trace form

\( 1376 q - 15 q^{2} - 5 q^{3} + 2685 q^{4} - 9 q^{6} - 13287 q^{9} + O(q^{10}) \) \( 1376 q - 15 q^{2} - 5 q^{3} + 2685 q^{4} - 9 q^{6} - 13287 q^{9} + 164 q^{10} - 9 q^{11} - 20 q^{12} - 10 q^{13} - 2956 q^{14} + 1311 q^{15} + 44849 q^{16} - 5 q^{17} - 9 q^{19} - 4044 q^{20} - 730 q^{22} - 4615 q^{23} + 1242 q^{24} + 16340 q^{25} - 8284 q^{26} - 20 q^{27} - 15 q^{28} + 887 q^{29} + 2665 q^{30} - 11085 q^{33} - 13156 q^{35} - 196489 q^{36} - 151785 q^{37} - 20 q^{38} + 13912 q^{39} + 143792 q^{40} + 65178 q^{41} + 77755 q^{42} - 14637 q^{45} + 42531 q^{46} + 140140 q^{48} - 1459816 q^{49} - 215373 q^{50} + 281072 q^{51} - 64975 q^{52} - 210160 q^{53} - 180165 q^{54} - 71106 q^{55} + 34662 q^{56} - 574395 q^{58} - 5751 q^{59} + 33505 q^{61} + 208145 q^{62} - 639900 q^{63} - 1432348 q^{64} + 99069 q^{65} + 4432 q^{66} - 15 q^{67} - 114882 q^{69} - 9 q^{71} - 15375 q^{72} - 496832 q^{74} - 152312 q^{75} + 152814 q^{76} + 602090 q^{77} - 444120 q^{78} - 221324 q^{79} + 1074777 q^{80} + 1214431 q^{81} + 191766 q^{84} + 94233 q^{85} + 27785 q^{87} + 796895 q^{88} - 68814 q^{89} + 590554 q^{90} - 153691 q^{91} + 2996680 q^{92} + 406989 q^{94} - 381139 q^{95} - 15 q^{97} - 366630 q^{98} + O(q^{100}) \)

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.