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Properties

Label 605.6.s
Level $605$
Weight $6$
Character orbit 605.s
Rep. character $\chi_{605}(16,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $8800$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.s (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 13280 8800 4480
Cusp forms 13120 8800 4320
Eisenstein series 160 0 160

Trace form

\( 8800 q + 4 q^{2} - 44 q^{3} + 3476 q^{4} - 24 q^{6} + 196 q^{7} + 932 q^{8} - 178662 q^{9} + O(q^{10}) \) \( 8800 q + 4 q^{2} - 44 q^{3} + 3476 q^{4} - 24 q^{6} + 196 q^{7} + 932 q^{8} - 178662 q^{9} - 800 q^{10} - 1038 q^{11} + 9504 q^{12} + 3504 q^{13} - 3498 q^{14} + 7700 q^{15} + 62612 q^{16} + 1108 q^{17} + 574 q^{18} - 4262 q^{19} - 1408 q^{21} - 26404 q^{22} - 9460 q^{23} - 37836 q^{24} + 137500 q^{25} + 20064 q^{26} + 46420 q^{27} + 17618 q^{28} + 14634 q^{29} - 8000 q^{30} - 43868 q^{31} - 96252 q^{32} - 39434 q^{33} - 45276 q^{34} + 12700 q^{35} + 327052 q^{36} + 41316 q^{37} + 46838 q^{38} + 31738 q^{39} - 96000 q^{40} - 25584 q^{41} - 133254 q^{42} - 56276 q^{43} - 306404 q^{44} + 102138 q^{46} - 36828 q^{47} + 286 q^{48} + 491502 q^{49} + 2500 q^{50} + 208836 q^{51} + 355294 q^{52} - 216920 q^{53} - 325366 q^{54} + 53700 q^{55} + 139898 q^{56} + 392504 q^{57} - 376464 q^{58} + 17754 q^{59} - 58850 q^{60} - 58988 q^{61} + 148662 q^{62} - 88834 q^{63} + 211640 q^{64} - 154600 q^{65} - 794354 q^{66} - 74734 q^{67} - 161574 q^{68} + 174570 q^{69} - 9900 q^{70} - 149072 q^{71} - 388974 q^{72} + 364154 q^{73} + 353200 q^{74} + 41250 q^{75} + 1023040 q^{76} + 500990 q^{77} - 941688 q^{78} + 1103550 q^{79} - 72600 q^{80} - 14841640 q^{81} + 659076 q^{82} + 93062 q^{83} - 323208 q^{84} - 50750 q^{85} - 629024 q^{86} + 67148 q^{87} + 1214048 q^{88} + 719928 q^{89} + 721800 q^{90} + 239756 q^{91} - 85052 q^{92} - 1654950 q^{93} - 196720 q^{94} + 144400 q^{95} + 100926 q^{96} + 660198 q^{97} + 1273604 q^{98} + 876496 q^{99} + O(q^{100}) \)

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

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