Space of modular forms of level 3150, weight 2, and Character 3150.dv

• Label: 3150.2.dv
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.dv
• Rep. character: $\chi_{3150}(109,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $800$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.dv (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 175 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

	Total	New	Old
Modular forms	5888	800	5088
Cusp forms	5632	800	4832
Eisenstein series	256	0	256

Trace form

800 * q - 100 * q^4 - 2 * q^5 + 2 * q^10 - 6 * q^11 + 100 * q^16 - 20 * q^17 + 4 * q^19 - 4 * q^20 - 40 * q^22 - 30 * q^23 - 12 * q^25 - 48 * q^26 + 10 * q^28 + 24 * q^29 + 6 * q^31 - 16 * q^34 - 4 * q^35 - 2 * q^40 + 4 * q^41 - 4 * q^44 - 12 * q^46 - 16 * q^50 - 20 * q^53 + 16 * q^55 - 8 * q^61 + 120 * q^62 + 200 * q^64 - 34 * q^65 - 10 * q^70 - 4 * q^71 + 40 * q^73 + 16 * q^74 - 32 * q^76 + 80 * q^77 - 2 * q^80 + 120 * q^83 - 68 * q^85 + 12 * q^86 + 10 * q^88 - 54 * q^89 + 4 * q^91 + 40 * q^92 + 32 * q^94 + 44 * q^95 + 20 * q^97 + 40 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)