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

• Label: 1650.2.cn
• Level: $1650$
• Weight: $2$
• Character orbit: 1650.cn
• Rep. character: $\chi_{1650}(7,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $288$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.cn (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	3072	288	2784
Cusp forms	2688	288	2400
Eisenstein series	384	0	384

Trace form

288 * q - 40 * q^7 + 16 * q^11 + 72 * q^16 - 40 * q^17 - 4 * q^22 + 16 * q^23 + 32 * q^26 - 20 * q^28 + 32 * q^31 - 12 * q^33 + 72 * q^36 + 32 * q^37 - 80 * q^41 + 12 * q^42 + 80 * q^46 + 88 * q^47 + 160 * q^51 + 40 * q^52 + 72 * q^53 - 32 * q^56 + 80 * q^57 + 12 * q^58 + 160 * q^61 + 80 * q^62 + 40 * q^63 + 64 * q^66 - 80 * q^67 + 40 * q^68 - 20 * q^73 + 72 * q^81 + 16 * q^82 + 64 * q^86 - 4 * q^88 + 80 * q^91 - 16 * q^92 - 24 * q^93 + 96 * q^97

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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)