Space of modular forms of level 570, weight 4, and Character 570.v

• Label: 570.4.v
• Level: $570$
• Weight: $4$
• Character orbit: 570.v
• Rep. character: $\chi_{570}(83,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $480$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(570, [\chi])\).

	Total	New	Old
Modular forms	1472	480	992
Cusp forms	1408	480	928
Eisenstein series	64	0	64

Trace form

480 * q + 192 * q^13 - 168 * q^15 + 3840 * q^16 - 64 * q^18 + 144 * q^22 - 72 * q^25 + 528 * q^27 + 576 * q^31 - 204 * q^33 - 432 * q^37 + 1216 * q^42 + 720 * q^43 - 2816 * q^45 + 1096 * q^51 - 768 * q^52 + 552 * q^55 - 824 * q^57 + 352 * q^60 + 1728 * q^61 + 1564 * q^63 + 944 * q^66 + 552 * q^67 - 1008 * q^70 - 128 * q^72 - 288 * q^73 + 6576 * q^75 + 1152 * q^76 + 1408 * q^78 - 1680 * q^81 + 3312 * q^85 + 56 * q^87 - 1152 * q^88 + 3176 * q^90 - 480 * q^91 - 860 * q^93 - 1152 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(570, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)