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

• Label: 605.6.b
• Level: $605$
• Weight: $6$
• Character orbit: 605.b
• Rep. character: $\chi_{605}(364,\cdot)$
• Character field: $\Q$
• Dimension: $264$
• Sturm bound: $396$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Sturm bound:			\(396\)

Dimensions

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

	Total	New	Old
Modular forms	342	282	60
Cusp forms	318	264	54
Eisenstein series	24	18	6

Trace form

264 * q - 4084 * q^4 - 8 * q^5 - 4 * q^6 - 20324 * q^9 - 430 * q^10 + 308 * q^14 - 1918 * q^15 + 62620 * q^16 + 520 * q^19 + 1356 * q^20 - 7852 * q^21 + 7112 * q^24 + 3332 * q^25 + 9120 * q^26 - 5184 * q^29 - 19834 * q^30 + 13928 * q^31 + 15128 * q^34 + 18342 * q^35 + 275008 * q^36 + 7696 * q^39 - 17668 * q^40 - 3600 * q^41 + 5014 * q^45 - 8524 * q^46 - 554380 * q^49 + 40918 * q^50 - 39780 * q^51 - 36732 * q^54 - 40496 * q^56 - 1040 * q^59 + 161920 * q^60 - 127824 * q^61 - 984828 * q^64 + 76880 * q^65 - 145972 * q^69 + 108412 * q^70 + 115256 * q^71 + 239452 * q^74 + 2826 * q^75 - 131240 * q^76 - 5364 * q^79 + 193224 * q^80 + 1082448 * q^81 + 636792 * q^84 - 185102 * q^85 - 73804 * q^86 + 133024 * q^89 + 169768 * q^90 + 209256 * q^91 + 470296 * q^94 - 240132 * q^95 - 614888 * q^96

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

\( S_{6}^{\mathrm{old}}(605, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)