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Properties

Label 325.6.z
Level $325$
Weight $6$
Character orbit 325.z
Rep. character $\chi_{325}(8,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1384$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.z (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 1416 1416 0
Cusp forms 1384 1384 0
Eisenstein series 32 32 0

Trace form

\( 1384 q + 2 q^{2} - 16 q^{3} - 5472 q^{4} + 90 q^{5} - 6 q^{6} + 506 q^{8} - 20 q^{9} + O(q^{10}) \) \( 1384 q + 2 q^{2} - 16 q^{3} - 5472 q^{4} + 90 q^{5} - 6 q^{6} + 506 q^{8} - 20 q^{9} + 128 q^{10} - 6 q^{11} + 920 q^{12} + 646 q^{13} - 20 q^{14} - 2050 q^{15} - 85516 q^{16} + 1414 q^{17} - 8790 q^{19} - 10870 q^{20} + 2424 q^{21} - 2228 q^{22} + 8700 q^{23} + 1100 q^{24} + 914 q^{25} - 16 q^{26} - 6040 q^{27} + 10230 q^{28} + 14160 q^{29} - 13216 q^{30} - 6 q^{31} - 27556 q^{32} + 20532 q^{33} - 42082 q^{34} - 15124 q^{35} + 640 q^{36} + 101170 q^{37} + 128 q^{38} + 7150 q^{39} - 68928 q^{40} + 44014 q^{41} + 25460 q^{42} - 1764 q^{43} + 118 q^{44} + 117668 q^{45} - 6 q^{46} - 51060 q^{47} + 30396 q^{48} - 3092488 q^{49} + 206916 q^{50} + 126848 q^{52} - 35726 q^{53} - 64594 q^{54} - 65876 q^{55} + 336140 q^{56} + 68320 q^{57} - 382930 q^{58} - 10 q^{59} + 154266 q^{60} - 12 q^{61} + 129860 q^{62} + 208090 q^{63} - 1302912 q^{64} - 495866 q^{65} - 12 q^{66} - 211190 q^{67} + 330188 q^{68} - 14028 q^{70} - 6 q^{71} + 12660 q^{72} + 139934 q^{73} + 239264 q^{75} + 4080 q^{76} + 91800 q^{77} - 1099570 q^{78} - 20 q^{79} + 1130216 q^{80} + 2060142 q^{81} + 808664 q^{82} + 470320 q^{83} + 99988 q^{84} - 204822 q^{85} + 314 q^{86} - 173316 q^{87} - 178976 q^{88} + 505390 q^{89} + 693480 q^{90} + 292924 q^{91} + 392176 q^{92} + 385740 q^{94} - 415728 q^{95} + 518424 q^{96} + 232014 q^{97} + 1043732 q^{98} + 972 q^{99} + O(q^{100}) \)

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.