Space of modular forms of level 880, weight 3, and Character 880.r

• Label: 880.3.r
• Level: $880$
• Weight: $3$
• Character orbit: 880.r
• Rep. character: $\chi_{880}(573,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $480$
• Sturm bound: $432$

Defining parameters

Level:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	880.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(880, [\chi])\).

	Total	New	Old
Modular forms	584	480	104
Cusp forms	568	480	88
Eisenstein series	16	0	16

Trace form

480 * q - 8 * q^4 + 12 * q^8 - 1440 * q^9 - 56 * q^16 - 28 * q^18 - 64 * q^19 - 84 * q^20 - 140 * q^28 - 56 * q^30 + 120 * q^32 + 104 * q^34 - 96 * q^35 + 96 * q^36 + 384 * q^38 - 40 * q^40 + 160 * q^42 - 224 * q^46 - 648 * q^48 + 192 * q^51 + 172 * q^52 - 328 * q^58 - 64 * q^59 - 76 * q^60 + 64 * q^61 + 252 * q^62 + 352 * q^64 + 576 * q^67 + 468 * q^68 + 192 * q^69 + 32 * q^70 - 700 * q^72 - 96 * q^73 - 32 * q^74 + 224 * q^75 - 512 * q^76 - 864 * q^78 - 208 * q^80 + 4320 * q^81 + 160 * q^82 - 72 * q^84 + 88 * q^86 + 264 * q^88 - 56 * q^90 - 192 * q^91 + 328 * q^92 + 152 * q^94 - 768 * q^95 - 504 * q^96 - 456 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(880, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(880, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(880, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)