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Properties

Label 605.6.g
Level $605$
Weight $6$
Character orbit 605.g
Rep. character $\chi_{605}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $720$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(605, [\chi])\).

Total New Old
Modular forms 1368 720 648
Cusp forms 1272 720 552
Eisenstein series 96 0 96

Trace form

\( 720 q + 4 q^{2} - 44 q^{3} - 2924 q^{4} - 24 q^{6} + 196 q^{7} + 932 q^{8} - 15042 q^{9} + O(q^{10}) \) \( 720 q + 4 q^{2} - 44 q^{3} - 2924 q^{4} - 24 q^{6} + 196 q^{7} + 932 q^{8} - 15042 q^{9} - 800 q^{10} - 2112 q^{12} + 1282 q^{13} - 322 q^{14} + 1650 q^{15} - 40548 q^{16} + 1108 q^{17} + 574 q^{18} - 4262 q^{19} - 3800 q^{20} - 1408 q^{21} - 8872 q^{23} + 6604 q^{24} - 112500 q^{25} + 11576 q^{26} + 46420 q^{27} + 17618 q^{28} + 14634 q^{29} - 8000 q^{30} - 14360 q^{31} - 96252 q^{32} - 76732 q^{34} + 12700 q^{35} - 143788 q^{36} + 38900 q^{37} + 52750 q^{38} + 31738 q^{39} + 9600 q^{40} - 25584 q^{41} - 187310 q^{42} - 56276 q^{43} + 102138 q^{46} - 35404 q^{47} - 93754 q^{48} - 406982 q^{49} + 2500 q^{50} - 19414 q^{51} + 52706 q^{52} + 124812 q^{53} + 98904 q^{54} + 441888 q^{56} - 200550 q^{57} + 64594 q^{58} + 9906 q^{59} - 58850 q^{60} - 58988 q^{61} - 293648 q^{62} - 88834 q^{63} - 715400 q^{64} - 154600 q^{65} + 310216 q^{67} - 161574 q^{68} + 105594 q^{69} + 56300 q^{70} - 207320 q^{71} - 388974 q^{72} + 226830 q^{73} + 353200 q^{74} + 41250 q^{75} + 1077952 q^{76} + 74460 q^{78} + 131282 q^{79} - 194200 q^{80} - 1494692 q^{81} - 83228 q^{82} + 93062 q^{83} - 323208 q^{84} + 46600 q^{85} - 462184 q^{86} + 67148 q^{87} - 109232 q^{89} - 61400 q^{90} - 1031224 q^{91} - 148660 q^{92} - 1405192 q^{93} - 198480 q^{94} + 144400 q^{95} + 138942 q^{96} + 16708 q^{97} - 1260268 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)