Space of modular forms of level 1350, weight 2, and Character 1350.bc

• Label: 1350.2.bc
• Level: $1350$
• Weight: $2$
• Character orbit: 1350.bc
• Rep. character: $\chi_{1350}(31,\cdot)$
• Character field: $\Q(\zeta_{45})$
• Dimension: $2160$
• Sturm bound: $540$

Defining parameters

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.bc (of order \(45\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 675 \)
Character field:			\(\Q(\zeta_{45})\)
Sturm bound:			\(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

	Total	New	Old
Modular forms	6576	2160	4416
Cusp forms	6384	2160	4224
Eisenstein series	192	0	192

Trace form

2160 * q - 24 * q^5 - 42 * q^15 - 12 * q^20 - 72 * q^21 + 24 * q^23 - 72 * q^25 + 288 * q^26 + 12 * q^27 - 36 * q^30 + 36 * q^31 + 12 * q^33 - 18 * q^35 - 24 * q^36 + 36 * q^38 + 60 * q^39 + 48 * q^42 + 12 * q^44 + 174 * q^45 - 78 * q^47 - 18 * q^48 + 36 * q^50 + 120 * q^53 + 36 * q^54 + 36 * q^57 - 18 * q^59 + 18 * q^60 + 84 * q^63 + 270 * q^64 + 18 * q^65 + 108 * q^67 - 144 * q^68 - 48 * q^72 + 48 * q^75 + 336 * q^77 + 24 * q^78 - 36 * q^81 + 60 * q^83 - 282 * q^87 + 12 * q^89 + 30 * q^90 + 72 * q^92 + 48 * q^93 + 42 * q^95 - 72 * q^97 + 60 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)