Space of modular forms of level 720, weight 4, and Character 720.bd

• Label: 720.4.bd
• Level: $720$
• Weight: $4$
• Character orbit: 720.bd
• Rep. character: $\chi_{720}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $356$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(720, [\chi])\).

	Total	New	Old
Modular forms	880	364	516
Cusp forms	848	356	492
Eisenstein series	32	8	24

Trace form

356 * q + 2 * q^2 - 12 * q^4 + 2 * q^5 - 4 * q^7 + 44 * q^8 - 18 * q^10 + 4 * q^11 - 4 * q^13 + 128 * q^16 + 4 * q^17 + 24 * q^19 + 176 * q^20 - 72 * q^22 + 4 * q^23 - 268 * q^26 - 624 * q^28 - 288 * q^32 - 112 * q^34 + 24 * q^35 - 4 * q^37 - 604 * q^38 + 1872 * q^40 - 868 * q^43 - 1624 * q^44 + 20 * q^46 - 408 * q^47 + 698 * q^50 - 352 * q^52 - 4 * q^55 - 164 * q^56 - 2684 * q^58 + 688 * q^59 + 908 * q^61 + 740 * q^62 - 456 * q^64 + 4 * q^65 + 1844 * q^67 - 2680 * q^68 + 440 * q^70 - 216 * q^71 - 296 * q^73 - 1332 * q^74 + 1812 * q^76 + 3064 * q^80 + 1588 * q^82 - 252 * q^85 - 1028 * q^86 + 1312 * q^88 + 844 * q^91 + 2752 * q^92 - 1716 * q^94 + 1240 * q^95 - 4 * q^97 - 4854 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(720, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(720, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(720, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)