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Properties

Label 325.6.bg
Level $325$
Weight $6$
Character orbit 325.bg
Rep. character $\chi_{325}(36,\cdot)$
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.bg (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

\( 1392 q - 9 q^{2} - 3 q^{3} - 2787 q^{4} - 9 q^{6} - 24 q^{7} + 14091 q^{9} + O(q^{10}) \) \( 1392 q - 9 q^{2} - 3 q^{3} - 2787 q^{4} - 9 q^{6} - 24 q^{7} + 14091 q^{9} + 80 q^{10} - 9 q^{11} + 728 q^{12} + 2220 q^{13} - 3340 q^{14} - 1335 q^{15} + 40649 q^{16} + 411 q^{17} - 9 q^{19} - 27660 q^{20} + 3352 q^{22} + 2503 q^{23} - 1290 q^{24} - 5466 q^{25} + 12052 q^{26} + 9120 q^{27} + 183 q^{28} - 2063 q^{29} - 10963 q^{30} - 44538 q^{32} + 1953 q^{33} + 21530 q^{35} - 234205 q^{36} + 35964 q^{37} + 32852 q^{38} + 12940 q^{39} - 56824 q^{40} - 2346 q^{41} - 34009 q^{42} - 11032 q^{43} - 130122 q^{45} - 42549 q^{46} + 94952 q^{48} + 1632672 q^{49} - 227649 q^{50} - 281136 q^{51} + 254027 q^{52} - 4054 q^{53} - 175407 q^{54} + 52430 q^{55} - 30572 q^{56} + 186171 q^{58} - 5751 q^{59} - 14561 q^{61} + 64289 q^{62} - 226596 q^{63} + 1172324 q^{64} - 174373 q^{65} + 57752 q^{66} + 271647 q^{67} - 172550 q^{68} - 116826 q^{69} - 9 q^{71} - 467913 q^{72} - 500376 q^{74} - 244794 q^{75} - 152862 q^{76} - 207294 q^{77} + 924954 q^{78} - 221324 q^{79} - 873135 q^{80} + 845717 q^{81} - 111872 q^{82} - 110760 q^{84} - 102852 q^{85} + 124415 q^{87} + 657113 q^{88} - 68814 q^{89} - 351126 q^{90} + 153679 q^{91} - 1321548 q^{92} + 97914 q^{93} + 406861 q^{94} + 39305 q^{95} + 335151 q^{97} + 1091946 q^{98} + O(q^{100}) \)

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.