↑

Properties

Label 325.6.be
Level $325$
Weight $6$
Character orbit 325.be
Rep. character $\chi_{325}(47,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1384$
Sturm bound $210$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.be (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

\( 1384 q - 10 q^{2} - 16 q^{3} + 5472 q^{4} - 24 q^{5} - 6 q^{6} - 16 q^{7} - 10 q^{8} - 20 q^{9} + O(q^{10}) \) \( 1384 q - 10 q^{2} - 16 q^{3} + 5472 q^{4} - 24 q^{5} - 6 q^{6} - 16 q^{7} - 10 q^{8} - 20 q^{9} - 128 q^{10} - 6 q^{11} - 920 q^{12} + 280 q^{13} - 20 q^{14} + 2034 q^{15} - 85516 q^{16} - 1414 q^{17} - 7588 q^{18} - 8790 q^{19} + 4746 q^{20} - 2436 q^{21} - 2228 q^{22} - 8700 q^{23} - 1100 q^{24} - 914 q^{25} - 16 q^{26} - 6040 q^{27} - 6278 q^{28} + 14160 q^{29} + 13216 q^{30} - 6 q^{31} - 56940 q^{33} - 5738 q^{34} - 15124 q^{35} - 640 q^{36} - 18576 q^{37} - 128 q^{38} + 7150 q^{39} - 68928 q^{40} - 2126 q^{41} + 25460 q^{42} + 1764 q^{43} - 138 q^{44} - 46194 q^{45} - 6 q^{46} + 58212 q^{47} + 30396 q^{48} + 3092488 q^{49} + 134464 q^{50} - 307968 q^{52} - 35726 q^{53} - 67766 q^{54} - 65876 q^{55} - 336140 q^{56} + 277506 q^{58} - 10 q^{59} + 93006 q^{60} - 12 q^{61} - 129860 q^{62} - 167390 q^{63} + 1302912 q^{64} - 28332 q^{65} - 12 q^{66} - 10 q^{67} + 330188 q^{68} - 296108 q^{70} - 6 q^{71} - 540628 q^{72} - 166490 q^{73} - 239264 q^{75} + 4080 q^{76} - 91800 q^{77} + 543326 q^{78} - 20 q^{79} - 678728 q^{80} + 2060142 q^{81} - 808664 q^{82} + 290100 q^{83} - 100008 q^{84} - 374108 q^{85} - 326 q^{86} - 173316 q^{87} + 178976 q^{88} + 658540 q^{89} - 693480 q^{90} - 292936 q^{91} + 392176 q^{92} - 358440 q^{93} + 385740 q^{94} + 415728 q^{95} - 468516 q^{96} - 10 q^{97} + 1547620 q^{98} - 972 q^{99} + O(q^{100}) \)

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.