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Properties

Label 325.6.l
Level $325$
Weight $6$
Character orbit 325.l
Rep. character $\chi_{325}(66,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $600$
Sturm bound $210$

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Defining parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.l (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(210\)

Dimensions

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

Total New Old
Modular forms 704 600 104
Cusp forms 688 600 88
Eisenstein series 16 0 16

Trace form

\( 600 q - 4 q^{3} - 2400 q^{4} - 254 q^{5} - 144 q^{6} + 388 q^{7} + 738 q^{8} - 12274 q^{9} + O(q^{10}) \) \( 600 q - 4 q^{3} - 2400 q^{4} - 254 q^{5} - 144 q^{6} + 388 q^{7} + 738 q^{8} - 12274 q^{9} + 746 q^{10} - 1442 q^{11} + 1176 q^{12} + 2748 q^{14} + 380 q^{15} - 42228 q^{16} + 2214 q^{17} - 7588 q^{18} - 2888 q^{19} + 3964 q^{20} + 2580 q^{21} + 5608 q^{22} - 10894 q^{23} + 44420 q^{24} + 9400 q^{25} + 16224 q^{26} - 12952 q^{27} - 24764 q^{28} - 4254 q^{29} - 22138 q^{30} + 17268 q^{31} - 25384 q^{32} + 13292 q^{33} + 15360 q^{34} + 47206 q^{35} - 249076 q^{36} + 46252 q^{37} - 45664 q^{38} - 12168 q^{39} + 92014 q^{40} - 26896 q^{41} - 82652 q^{42} - 122856 q^{43} - 49534 q^{44} - 34620 q^{45} - 57344 q^{46} + 35100 q^{47} + 143684 q^{48} + 1508756 q^{49} - 62782 q^{50} + 32388 q^{51} - 39208 q^{52} + 54026 q^{53} - 46656 q^{54} - 81308 q^{55} - 131904 q^{56} - 514036 q^{57} - 104282 q^{58} - 99114 q^{59} - 141758 q^{60} - 58180 q^{61} - 111308 q^{62} - 151770 q^{63} - 529518 q^{64} + 338 q^{65} + 93550 q^{66} - 221442 q^{67} - 365096 q^{68} + 374210 q^{69} - 507804 q^{70} - 216126 q^{71} + 953414 q^{72} + 233540 q^{73} - 196472 q^{74} + 132060 q^{75} + 420020 q^{76} + 13908 q^{77} + 247108 q^{79} + 104388 q^{80} - 897828 q^{81} + 732356 q^{82} + 383866 q^{83} - 708624 q^{84} - 783094 q^{85} - 52500 q^{86} + 307968 q^{87} - 816814 q^{88} - 69656 q^{89} - 180790 q^{90} - 66248 q^{91} + 42352 q^{92} + 534952 q^{93} + 56320 q^{94} + 395338 q^{95} - 1397920 q^{96} + 890974 q^{97} + 79800 q^{98} + 1202744 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(325, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(325, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)