Space of modular forms of level 1650, weight 2, and Character 1650.q

• Label: 1650.2.q
• Level: $1650$
• Weight: $2$
• Character orbit: 1650.q
• Rep. character: $\chi_{1650}(181,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $240$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.q (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{5})\)
Sturm bound:			\(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1650, [\chi])\).

	Total	New	Old
Modular forms	1472	240	1232
Cusp forms	1408	240	1168
Eisenstein series	64	0	64

Trace form

240 * q - 60 * q^4 - 12 * q^5 + 4 * q^6 - 6 * q^7 + 240 * q^9 - 6 * q^10 - 12 * q^11 + 16 * q^13 - 8 * q^15 - 60 * q^16 - 4 * q^17 + 4 * q^19 - 12 * q^20 + 8 * q^21 + 12 * q^22 + 16 * q^23 + 4 * q^24 - 32 * q^25 - 6 * q^28 + 8 * q^30 - 2 * q^31 + 2 * q^33 + 20 * q^35 - 60 * q^36 - 16 * q^37 + 4 * q^40 - 12 * q^41 - 2 * q^42 + 32 * q^43 + 8 * q^44 - 12 * q^45 + 32 * q^46 + 96 * q^47 - 66 * q^49 + 16 * q^50 + 8 * q^51 + 16 * q^52 - 12 * q^53 + 4 * q^54 + 30 * q^55 + 28 * q^57 + 8 * q^58 - 12 * q^59 + 12 * q^60 - 48 * q^61 + 40 * q^62 - 6 * q^63 - 60 * q^64 + 44 * q^65 - 92 * q^67 - 4 * q^68 - 4 * q^69 + 48 * q^70 + 56 * q^71 - 8 * q^73 + 24 * q^75 - 16 * q^76 - 24 * q^77 - 2 * q^79 + 8 * q^80 + 240 * q^81 + 8 * q^82 + 64 * q^83 + 8 * q^84 + 8 * q^85 - 12 * q^86 + 24 * q^87 - 8 * q^88 - 6 * q^90 + 24 * q^91 - 24 * q^92 - 24 * q^93 + 32 * q^94 - 108 * q^95 - 16 * q^96 + 8 * q^97 - 16 * q^98 - 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1650, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1650, [\chi])\) into lower level spaces

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