Space of modular forms of level 360, weight 4, and Character 360.bk

• Label: 360.4.bk
• Level: $360$
• Weight: $4$
• Character orbit: 360.bk
• Rep. character: $\chi_{360}(229,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $424$
• Sturm bound: $288$

Defining parameters

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 360 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(360, [\chi])\).

	Total	New	Old
Modular forms	440	440	0
Cusp forms	424	424	0
Eisenstein series	16	16	0

Trace form

424 * q - 2 * q^4 + 12 * q^6 - 8 * q^9 + 12 * q^10 - 34 * q^14 + 50 * q^15 - 2 * q^16 - 206 * q^20 + 58 * q^24 - 2 * q^25 - 248 * q^26 - 612 * q^30 - 4 * q^31 - 184 * q^34 + 240 * q^36 + 100 * q^39 - 126 * q^40 - 4 * q^41 - 1448 * q^44 - 76 * q^46 + 9208 * q^49 - 1170 * q^50 - 182 * q^54 - 508 * q^55 + 26 * q^56 - 598 * q^60 - 692 * q^64 + 498 * q^65 - 4268 * q^66 + 84 * q^70 + 7936 * q^71 + 2292 * q^74 + 684 * q^76 - 4 * q^79 - 3012 * q^80 + 608 * q^81 + 1546 * q^84 + 1424 * q^86 + 832 * q^89 - 8836 * q^90 + 1622 * q^94 + 248 * q^95 - 434 * q^96

Decomposition of \(S_{4}^{\mathrm{new}}(360, [\chi])\) into newform subspaces

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