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

• Label: 3150.2.eh
• Level: $3150$
• Weight: $2$
• Character orbit: 3150.eh
• Rep. character: $\chi_{3150}(113,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $2880$
• Sturm bound: $1440$

Defining parameters

Level:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.eh (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 225 \)
Character field:			\(\Q(\zeta_{60})\)
Sturm bound:			\(1440\)

Dimensions

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

	Total	New	Old
Modular forms	11648	2880	8768
Cusp forms	11392	2880	8512
Eisenstein series	256	0	256

Trace form

2880 * q + 8 * q^3 - 8 * q^12 + 8 * q^15 - 360 * q^16 - 8 * q^18 - 24 * q^20 - 24 * q^23 + 96 * q^25 - 16 * q^27 - 8 * q^33 - 48 * q^37 + 72 * q^38 - 40 * q^39 + 80 * q^45 + 96 * q^47 + 16 * q^48 - 48 * q^55 + 32 * q^57 + 120 * q^59 + 40 * q^60 - 32 * q^63 - 24 * q^65 - 24 * q^67 - 16 * q^72 + 32 * q^75 + 168 * q^78 - 80 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 + 240 * q^87 + 40 * q^90 - 24 * q^92 + 72 * q^93 + 120 * q^95 - 72 * q^97

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)