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

• Label: 1650.2.bu
• Level: $1650$
• Weight: $2$
• Character orbit: 1650.bu
• Rep. character: $\chi_{1650}(101,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $304$
• Sturm bound: $720$

Defining parameters

Level:	\( N \)	\(=\)	\( 1650 = 2 \cdot 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1650.bu (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 33 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(720\)

Dimensions

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

	Total	New	Old
Modular forms	1536	304	1232
Cusp forms	1344	304	1040
Eisenstein series	192	0	192

Trace form

304 * q - 76 * q^4 - 5 * q^6 + 12 * q^9 + 10 * q^12 - 76 * q^16 - 5 * q^18 - 30 * q^19 + 5 * q^24 + 6 * q^27 - 10 * q^28 - 2 * q^31 - 31 * q^33 + 36 * q^34 - 3 * q^36 + 4 * q^37 + 50 * q^39 + 28 * q^42 + 20 * q^46 + 108 * q^49 + 25 * q^51 + 20 * q^52 - 45 * q^57 + 38 * q^58 + 60 * q^61 + 10 * q^63 - 76 * q^64 + 22 * q^66 - 20 * q^67 - 26 * q^69 - 20 * q^72 + 30 * q^73 - 80 * q^78 - 20 * q^79 + 8 * q^81 + 22 * q^82 - 40 * q^84 - 80 * q^91 + 82 * q^93 - 80 * q^94 + 66 * q^97 - 28 * 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

\( S_{2}^{\mathrm{old}}(1650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)