Properties

Label 490.6.w
Level $490$
Weight $6$
Character orbit 490.w
Rep. character $\chi_{490}(3,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3360$
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.w (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 10176 3360 6816
Cusp forms 9984 3360 6624
Eisenstein series 192 0 192

Trace form

\( 3360 q + 132 q^{5} + 560 q^{6} + 312 q^{7} + O(q^{10}) \) \( 3360 q + 132 q^{5} + 560 q^{6} + 312 q^{7} - 1488 q^{10} + 20 q^{11} - 2364 q^{15} - 71680 q^{16} - 8552 q^{17} + 4140 q^{21} + 7120 q^{22} - 1276 q^{23} - 4444 q^{25} - 3520 q^{26} + 6336 q^{28} + 3408 q^{30} - 4920 q^{31} - 73608 q^{33} - 35848 q^{35} + 756160 q^{36} - 5412 q^{37} + 2976 q^{38} + 217840 q^{41} + 192816 q^{42} + 92824 q^{43} - 19660 q^{45} - 258400 q^{46} - 276408 q^{47} - 51328 q^{50} - 271440 q^{51} - 561440 q^{53} + 317436 q^{55} + 170240 q^{56} - 59492 q^{57} + 107008 q^{58} - 98260 q^{61} + 264996 q^{63} - 73080 q^{65} - 59216 q^{67} - 51264 q^{68} - 461696 q^{70} + 38320 q^{71} - 491628 q^{73} + 570132 q^{75} - 155656 q^{77} - 83520 q^{78} + 33792 q^{80} - 1565380 q^{81} - 236352 q^{82} + 1708812 q^{83} - 339880 q^{85} - 115120 q^{86} + 265572 q^{87} - 22784 q^{88} + 379344 q^{90} - 941420 q^{91} + 40832 q^{92} + 959464 q^{93} + 385812 q^{95} + 61440 q^{96} + 68320 q^{98} + O(q^{100}) \)

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

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