Space of modular forms of level 1840, weight 2, and Character 1840.cw

• Label: 1840.2.cw
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.cw
• Rep. character: $\chi_{1840}(11,\cdot)$
• Character field: $\Q(\zeta_{44})$
• Dimension: $3840$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.cw (of order \(44\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 368 \)
Character field:			\(\Q(\zeta_{44})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1840, [\chi])\).

	Total	New	Old
Modular forms	5840	3840	2000
Cusp forms	5680	3840	1840
Eisenstein series	160	0	160

Trace form

3840 * q + 8 * q^4 - 12 * q^6 - 12 * q^12 - 32 * q^16 + 40 * q^18 + 16 * q^23 + 8 * q^24 + 24 * q^27 - 32 * q^29 + 44 * q^34 + 20 * q^36 - 220 * q^38 - 48 * q^39 - 356 * q^46 + 80 * q^48 + 384 * q^49 + 36 * q^50 - 64 * q^52 - 144 * q^54 + 144 * q^58 + 24 * q^59 + 60 * q^62 + 44 * q^64 - 16 * q^69 - 188 * q^72 - 144 * q^77 + 92 * q^78 + 384 * q^81 - 36 * q^82 - 32 * q^85 - 12 * q^92 + 480 * q^93 - 72 * q^94 + 136 * q^96 - 208 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(1840, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1840, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)