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Properties

Label 490.6.k
Level $490$
Weight $6$
Character orbit 490.k
Rep. character $\chi_{490}(71,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $576$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 490.k (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(490, [\chi])\).

Total New Old
Modular forms 2544 576 1968
Cusp forms 2496 576 1920
Eisenstein series 48 0 48

Trace form

\( 576 q + 36 q^{3} - 1536 q^{4} + 50 q^{5} + 200 q^{6} + 312 q^{7} - 7474 q^{9} + O(q^{10}) \) \( 576 q + 36 q^{3} - 1536 q^{4} + 50 q^{5} + 200 q^{6} + 312 q^{7} - 7474 q^{9} + 200 q^{10} + 20 q^{11} + 576 q^{12} + 580 q^{13} - 304 q^{14} - 24576 q^{16} + 144 q^{17} + 1984 q^{18} + 1060 q^{19} + 800 q^{20} + 5244 q^{21} - 4768 q^{22} + 660 q^{23} - 1280 q^{24} - 60000 q^{25} - 11176 q^{26} + 51924 q^{27} + 4992 q^{28} + 10942 q^{29} + 7600 q^{30} + 7160 q^{31} - 42368 q^{33} + 12224 q^{34} - 11800 q^{35} - 119584 q^{36} - 131736 q^{37} + 16448 q^{38} - 26724 q^{39} + 3200 q^{40} + 21236 q^{41} + 63872 q^{42} - 15712 q^{43} - 800 q^{44} + 6250 q^{45} - 35480 q^{46} + 11500 q^{47} - 55296 q^{48} - 93440 q^{49} - 82704 q^{51} + 14656 q^{52} + 49536 q^{53} + 6376 q^{54} - 7600 q^{55} + 44416 q^{56} + 84496 q^{57} + 161440 q^{58} + 27954 q^{59} - 462368 q^{61} - 54576 q^{62} - 553212 q^{63} - 393216 q^{64} - 21100 q^{65} + 109632 q^{66} - 127992 q^{67} - 256640 q^{68} - 353656 q^{69} - 36600 q^{70} + 54144 q^{71} + 31744 q^{72} - 217108 q^{73} - 206280 q^{74} + 22500 q^{75} + 16960 q^{76} - 84404 q^{77} - 153472 q^{78} + 111880 q^{79} - 76800 q^{80} - 1383758 q^{81} - 8800 q^{82} + 30008 q^{83} + 83904 q^{84} + 3800 q^{85} + 171504 q^{86} + 271112 q^{87} + 190720 q^{88} + 327164 q^{89} + 81000 q^{90} - 436682 q^{91} - 4224 q^{92} + 341104 q^{93} - 145688 q^{94} + 40400 q^{95} - 20480 q^{96} - 185880 q^{97} - 1171232 q^{98} - 2412764 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)