Space of modular forms of level 308, weight 4, and Character 308.be

• Label: 308.4.be
• Level: $308$
• Weight: $4$
• Character orbit: 308.be
• Rep. character: $\chi_{308}(3,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $1120$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	308.be (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 308 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(308, [\chi])\).

	Total	New	Old
Modular forms	1184	1184	0
Cusp forms	1120	1120	0
Eisenstein series	64	64	0

Trace form

1120 * q - 5 * q^2 - 13 * q^4 - 18 * q^5 - 80 * q^8 + 1182 * q^9 - 24 * q^10 - 24 * q^12 + 114 * q^14 + 175 * q^16 - 18 * q^17 + 154 * q^18 - 140 * q^21 - 1096 * q^22 + 639 * q^24 - 2938 * q^25 - 57 * q^26 + 86 * q^28 + 776 * q^29 - 107 * q^30 - 720 * q^32 - 60 * q^33 + 94 * q^36 + 18 * q^37 + 861 * q^38 + 741 * q^40 - 1240 * q^42 - 570 * q^44 - 372 * q^45 - 24 * q^46 + 708 * q^49 - 1494 * q^50 - 2877 * q^52 + 730 * q^53 - 5724 * q^54 + 4544 * q^56 - 240 * q^57 - 1280 * q^58 + 1255 * q^60 - 618 * q^61 + 3416 * q^64 - 236 * q^65 + 2607 * q^66 + 4413 * q^68 - 433 * q^70 - 304 * q^72 - 18 * q^73 - 339 * q^74 + 818 * q^77 - 5300 * q^78 - 9 * q^80 + 8850 * q^81 - 5889 * q^82 - 4171 * q^84 - 560 * q^85 + 1872 * q^86 + 995 * q^88 - 48 * q^89 - 8010 * q^92 + 1034 * q^93 + 8955 * q^94 - 9207 * q^96 + 13012 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

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