Space of modular forms of level 1020, weight 2, and Character 1020.bf

• Label: 1020.2.bf
• Level: $1020$
• Weight: $2$
• Character orbit: 1020.bf
• Rep. character: $\chi_{1020}(191,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $288$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bf (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 204 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1020, [\chi])\).

	Total	New	Old
Modular forms	448	288	160
Cusp forms	416	288	128
Eisenstein series	32	0	32

Trace form

288 * q + 4 * q^10 - 20 * q^12 - 8 * q^16 + 24 * q^22 - 20 * q^24 + 24 * q^28 - 16 * q^33 + 28 * q^34 - 28 * q^40 - 56 * q^46 + 48 * q^52 - 20 * q^54 + 48 * q^57 - 32 * q^58 - 32 * q^61 + 24 * q^64 + 32 * q^69 - 104 * q^72 - 48 * q^73 - 108 * q^78 + 80 * q^81 + 48 * q^82 + 72 * q^84 - 80 * q^88 - 16 * q^96 - 48 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(1020, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1020, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 2}\)