Space of modular forms of level 2700, weight 2, and Character 2700.cb

• Label: 2700.2.cb
• Level: $2700$
• Weight: $2$
• Character orbit: 2700.cb
• Rep. character: $\chi_{2700}(7,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $3840$
• Sturm bound: $1080$

Defining parameters

Level:	\( N \)	\(=\)	\( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2700.cb (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 540 \)
Character field:			\(\Q(\zeta_{36})\)
Sturm bound:			\(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

	Total	New	Old
Modular forms	6624	3936	2688
Cusp forms	6336	3840	2496
Eisenstein series	288	96	192

Trace form

3840 * q + 12 * q^2 - 24 * q^6 + 6 * q^8 + 12 * q^12 + 24 * q^13 - 24 * q^16 + 12 * q^17 - 30 * q^18 - 48 * q^21 + 12 * q^22 - 48 * q^26 + 24 * q^28 + 72 * q^32 + 24 * q^33 - 24 * q^36 + 12 * q^37 - 48 * q^41 + 72 * q^42 - 12 * q^46 + 12 * q^48 + 12 * q^52 + 48 * q^53 + 312 * q^56 - 12 * q^57 + 12 * q^58 - 48 * q^61 + 6 * q^62 + 168 * q^66 + 36 * q^68 + 60 * q^72 + 12 * q^73 + 24 * q^76 + 24 * q^77 + 54 * q^78 - 48 * q^81 + 24 * q^82 + 192 * q^86 + 60 * q^88 + 126 * q^92 + 168 * q^93 + 192 * q^96 + 24 * q^97 - 108 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)