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

• Label: 605.6.m
• Level: $605$
• Weight: $6$
• Character orbit: 605.m
• Rep. character: $\chi_{605}(112,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $2096$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(396\)

Dimensions

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

	Total	New	Old
Modular forms	2736	2224	512
Cusp forms	2544	2096	448
Eisenstein series	192	128	64

Trace form

2096 * q + 10 * q^2 + 2 * q^3 - 38 * q^5 + 20 * q^6 + 600 * q^7 + 10 * q^8 + 1596 * q^12 + 10 * q^13 + 5018 * q^15 + 123388 * q^16 - 1900 * q^17 + 10 * q^18 + 1296 * q^20 - 29184 * q^23 + 9830 * q^25 + 8412 * q^26 + 7694 * q^27 + 18250 * q^28 - 6830 * q^30 + 9692 * q^31 + 10 * q^35 + 632028 * q^36 + 11614 * q^37 + 86250 * q^38 + 10250 * q^40 - 72280 * q^41 + 38470 * q^42 - 104188 * q^45 - 219380 * q^46 - 84820 * q^47 - 41286 * q^48 + 14250 * q^50 + 299820 * q^51 - 28350 * q^52 + 53144 * q^53 + 423304 * q^56 + 359570 * q^57 - 229894 * q^58 - 452102 * q^60 - 113780 * q^61 - 496200 * q^62 - 241370 * q^63 - 746352 * q^67 + 121930 * q^68 + 169754 * q^70 - 115388 * q^71 + 527620 * q^72 - 49250 * q^73 - 101162 * q^75 + 1377844 * q^78 + 520322 * q^80 + 2214148 * q^81 - 245706 * q^82 - 316090 * q^83 + 274770 * q^85 + 856812 * q^86 + 1102820 * q^90 - 371668 * q^91 + 534160 * q^92 - 84334 * q^93 - 701360 * q^95 - 2818080 * q^96 - 959306 * q^97

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

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