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

• Label: 1840.2.x
• Level: $1840$
• Weight: $2$
• Character orbit: 1840.x
• Rep. character: $\chi_{1840}(461,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $352$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1840.x (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 16 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(576\)

Dimensions

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

	Total	New	Old
Modular forms	584	352	232
Cusp forms	568	352	216
Eisenstein series	16	0	16

Trace form

352 * q + 12 * q^6 + 12 * q^12 - 16 * q^14 + 40 * q^18 - 16 * q^20 + 48 * q^22 - 8 * q^24 + 32 * q^26 - 24 * q^27 + 48 * q^28 - 40 * q^34 - 12 * q^36 - 40 * q^42 - 72 * q^44 + 80 * q^47 - 352 * q^49 + 80 * q^51 - 48 * q^52 - 32 * q^54 + 56 * q^56 + 20 * q^58 - 8 * q^59 + 56 * q^60 + 76 * q^62 - 12 * q^64 - 80 * q^66 + 16 * q^70 - 36 * q^72 + 40 * q^74 - 60 * q^78 - 32 * q^80 - 352 * q^81 + 116 * q^82 - 80 * q^83 + 32 * q^84 + 16 * q^86 - 40 * q^88 - 72 * q^90 - 64 * q^91 + 48 * q^93 - 48 * q^94 - 64 * q^95 + 120 * q^96 - 56 * q^98 - 64 * q^99

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

\( S_{2}^{\mathrm{old}}(1840, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(368, [\chi])\)\(^{\oplus 2}\)