Space of modular forms of level 490, weight 6, and Character 490.e

• Label: 490.6.e
• Level: $490$
• Weight: $6$
• Character orbit: 490.e
• Rep. character: $\chi_{490}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $136$
• Sturm bound: $504$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(504\)

Dimensions

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

	Total	New	Old
Modular forms	872	136	736
Cusp forms	808	136	672
Eisenstein series	64	0	64

Trace form

136 * q - 1088 * q^4 - 50 * q^5 + 80 * q^6 - 6462 * q^9 - 200 * q^10 + 770 * q^11 + 6720 * q^13 - 4400 * q^15 - 17408 * q^16 - 3396 * q^17 + 992 * q^18 + 1026 * q^19 + 1600 * q^20 + 4768 * q^22 - 132 * q^23 - 640 * q^24 - 42500 * q^25 - 7128 * q^26 + 16104 * q^27 + 8668 * q^29 + 3800 * q^30 + 8360 * q^31 + 14744 * q^33 - 12224 * q^34 + 206784 * q^36 + 59908 * q^37 - 17152 * q^38 + 23396 * q^39 - 3200 * q^40 - 13456 * q^41 + 100936 * q^43 + 12320 * q^44 - 15100 * q^45 + 12816 * q^46 - 2300 * q^47 - 75084 * q^51 - 53760 * q^52 - 37068 * q^53 - 88312 * q^54 + 7600 * q^55 + 116136 * q^57 + 26528 * q^58 + 42036 * q^59 + 35200 * q^60 + 62298 * q^61 + 215872 * q^62 + 557056 * q^64 - 98350 * q^65 - 40320 * q^66 - 119568 * q^67 - 54336 * q^68 - 193948 * q^69 - 426848 * q^71 + 15872 * q^72 + 127988 * q^73 - 21320 * q^74 - 32832 * q^76 + 263936 * q^78 - 227248 * q^79 - 12800 * q^80 - 604028 * q^81 - 11264 * q^82 - 99872 * q^83 + 67000 * q^85 + 144984 * q^86 - 156024 * q^87 - 38144 * q^88 + 40998 * q^89 + 162000 * q^90 + 4224 * q^92 + 554188 * q^93 + 231816 * q^94 + 96000 * q^95 - 10240 * q^96 - 188896 * q^97 - 398740 * q^99

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

\( S_{6}^{\mathrm{old}}(490, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)