Space of modular forms of level 605, weight 6, and Character 605.g

• Label: 605.6.g
• Level: $605$
• Weight: $6$
• Character orbit: 605.g
• Rep. character: $\chi_{605}(81,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $720$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(396\)

Dimensions

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

	Total	New	Old
Modular forms	1368	720	648
Cusp forms	1272	720	552
Eisenstein series	96	0	96

Trace form

720 * q + 4 * q^2 - 44 * q^3 - 2924 * q^4 - 24 * q^6 + 196 * q^7 + 932 * q^8 - 15042 * q^9 - 800 * q^10 - 2112 * q^12 + 1282 * q^13 - 322 * q^14 + 1650 * q^15 - 40548 * q^16 + 1108 * q^17 + 574 * q^18 - 4262 * q^19 - 3800 * q^20 - 1408 * q^21 - 8872 * q^23 + 6604 * q^24 - 112500 * q^25 + 11576 * q^26 + 46420 * q^27 + 17618 * q^28 + 14634 * q^29 - 8000 * q^30 - 14360 * q^31 - 96252 * q^32 - 76732 * q^34 + 12700 * q^35 - 143788 * q^36 + 38900 * q^37 + 52750 * q^38 + 31738 * q^39 + 9600 * q^40 - 25584 * q^41 - 187310 * q^42 - 56276 * q^43 + 102138 * q^46 - 35404 * q^47 - 93754 * q^48 - 406982 * q^49 + 2500 * q^50 - 19414 * q^51 + 52706 * q^52 + 124812 * q^53 + 98904 * q^54 + 441888 * q^56 - 200550 * q^57 + 64594 * q^58 + 9906 * q^59 - 58850 * q^60 - 58988 * q^61 - 293648 * q^62 - 88834 * q^63 - 715400 * q^64 - 154600 * q^65 + 310216 * q^67 - 161574 * q^68 + 105594 * q^69 + 56300 * q^70 - 207320 * q^71 - 388974 * q^72 + 226830 * q^73 + 353200 * q^74 + 41250 * q^75 + 1077952 * q^76 + 74460 * q^78 + 131282 * q^79 - 194200 * q^80 - 1494692 * q^81 - 83228 * q^82 + 93062 * q^83 - 323208 * q^84 + 46600 * q^85 - 462184 * q^86 + 67148 * q^87 - 109232 * q^89 - 61400 * q^90 - 1031224 * q^91 - 148660 * q^92 - 1405192 * q^93 - 198480 * q^94 + 144400 * q^95 + 138942 * q^96 + 16708 * q^97 - 1260268 * q^98

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

\( S_{6}^{\mathrm{old}}(605, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)