Space of modular forms of level 1650, weight 4, and Character 1650.cm

• Label: 1650.4.cm
• Level: $1650$
• Weight: $4$
• Character orbit: 1650.cm
• Rep. character: $\chi_{1650}(337,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $1440$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1650.cm (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1650, [\chi])\).

	Total	New	Old
Modular forms	8704	1440	7264
Cusp forms	8576	1440	7136
Eisenstein series	128	0	128

Trace form

1440 * q + 96 * q^5 - 140 * q^7 - 120 * q^10 - 168 * q^15 + 5760 * q^16 + 1280 * q^17 + 240 * q^19 - 312 * q^22 + 112 * q^23 - 1560 * q^25 - 240 * q^28 + 396 * q^33 + 12960 * q^36 - 1584 * q^37 + 816 * q^42 + 3424 * q^47 - 60 * q^49 + 3744 * q^53 - 1436 * q^55 - 336 * q^58 - 4080 * q^59 - 384 * q^60 + 160 * q^62 + 7080 * q^67 + 5120 * q^68 + 6240 * q^69 + 4272 * q^70 - 3420 * q^73 - 816 * q^75 + 7800 * q^77 + 420 * q^79 + 1024 * q^80 - 116640 * q^81 + 2688 * q^82 + 6840 * q^85 + 1632 * q^88 + 672 * q^92 - 1368 * q^93 + 4968 * q^97 - 13120 * q^98 + 5040 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1650, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)