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

• Label: 1650.4.m
• Level: $1650$
• Weight: $4$
• Character orbit: 1650.m
• Rep. character: $\chi_{1650}(361,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $720$
• Sturm bound: $1440$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	4352	720	3632
Cusp forms	4288	720	3568
Eisenstein series	64	0	64

Trace form

720 * q - 720 * q^4 - 32 * q^5 - 24 * q^6 + 38 * q^7 - 1620 * q^9 + 24 * q^10 + 112 * q^11 + 288 * q^13 + 36 * q^15 - 2880 * q^16 - 128 * q^17 - 176 * q^19 - 128 * q^20 - 168 * q^21 - 396 * q^22 + 28 * q^23 - 96 * q^24 + 214 * q^25 - 48 * q^28 + 48 * q^30 - 828 * q^31 - 594 * q^33 + 104 * q^35 - 6480 * q^36 - 912 * q^37 + 96 * q^40 - 768 * q^41 - 1224 * q^42 + 2256 * q^43 + 448 * q^44 - 288 * q^45 - 952 * q^46 - 4328 * q^47 - 9306 * q^49 + 816 * q^50 - 408 * q^51 - 768 * q^52 + 624 * q^53 - 216 * q^54 - 12 * q^55 + 36 * q^57 + 504 * q^58 + 408 * q^59 + 624 * q^60 - 3272 * q^61 + 680 * q^62 - 108 * q^63 - 11520 * q^64 + 5796 * q^65 - 5284 * q^67 + 2048 * q^68 + 2496 * q^69 - 2016 * q^71 - 2664 * q^73 - 216 * q^75 + 1856 * q^76 + 3812 * q^77 + 168 * q^79 + 768 * q^80 - 14580 * q^81 - 784 * q^82 - 3428 * q^83 - 672 * q^84 - 2020 * q^85 + 672 * q^86 - 3072 * q^87 + 1536 * q^88 + 216 * q^90 + 6576 * q^91 + 112 * q^92 + 1368 * q^93 - 3008 * q^94 - 1880 * q^95 - 384 * q^96 - 1014 * q^97 - 5248 * q^98 + 1008 * 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

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