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Properties

Label 490.6.q
Level $490$
Weight $6$
Character orbit 490.q
Rep. character $\chi_{490}(11,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1104$
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.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 5088 1104 3984
Cusp forms 4992 1104 3888
Eisenstein series 96 0 96

Trace form

\( 1104 q + 1472 q^{4} - 50 q^{5} - 200 q^{6} + 152 q^{7} + 5608 q^{9} + O(q^{10}) \) \( 1104 q + 1472 q^{4} - 50 q^{5} - 200 q^{6} + 152 q^{7} + 5608 q^{9} - 200 q^{10} + 10 q^{11} + 6720 q^{13} + 184 q^{14} + 23552 q^{16} - 3396 q^{17} + 992 q^{18} + 1026 q^{19} + 1600 q^{20} + 9306 q^{21} + 4768 q^{22} - 1056 q^{23} - 640 q^{24} + 57500 q^{25} - 10208 q^{26} - 40260 q^{27} - 6976 q^{28} - 10942 q^{29} + 3800 q^{30} + 8360 q^{31} + 14744 q^{33} - 12224 q^{34} + 11800 q^{35} - 243296 q^{36} - 118396 q^{37} - 19616 q^{38} + 120324 q^{39} - 3200 q^{40} + 95464 q^{41} + 148672 q^{42} - 26344 q^{43} - 2080 q^{44} - 15100 q^{45} - 117280 q^{46} - 365992 q^{47} - 212810 q^{49} - 150972 q^{51} - 72128 q^{52} + 70212 q^{53} + 47768 q^{54} + 7600 q^{55} + 82304 q^{56} - 310792 q^{57} + 419744 q^{58} + 327426 q^{59} + 524914 q^{61} - 109152 q^{62} - 584208 q^{63} - 753664 q^{64} - 10550 q^{65} - 40320 q^{66} + 81352 q^{67} + 204608 q^{68} + 27196 q^{69} + 36600 q^{70} - 54144 q^{71} + 15872 q^{72} + 416864 q^{73} + 194640 q^{74} - 32832 q^{76} + 428228 q^{77} + 153472 q^{78} + 202968 q^{79} + 76800 q^{80} - 486310 q^{81} - 11264 q^{82} + 8404 q^{83} - 206208 q^{84} - 3800 q^{85} + 85752 q^{86} + 1754920 q^{87} - 305152 q^{88} + 377026 q^{89} + 162000 q^{90} + 645834 q^{91} + 4224 q^{92} + 268580 q^{93} + 552416 q^{94} + 20200 q^{95} - 10240 q^{96} - 1242704 q^{97} + 1048448 q^{98} + 2412764 q^{99} + O(q^{100}) \)

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

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