Space of modular forms of level 312, weight 6, and Character 312.bb

• Label: 312.6.bb
• Level: $312$
• Weight: $6$
• Character orbit: 312.bb
• Rep. character: $\chi_{312}(61,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $280$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	312.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(312, [\chi])\).

	Total	New	Old
Modular forms	568	280	288
Cusp forms	552	280	272
Eisenstein series	16	0	16

Trace form

280 * q + 11340 * q^9 + 284 * q^10 - 792 * q^12 - 2480 * q^14 - 516 * q^16 - 404 * q^17 + 3020 * q^20 + 4200 * q^22 + 108 * q^24 - 168768 * q^25 - 30920 * q^26 - 3056 * q^28 - 684 * q^30 - 18520 * q^32 - 6232 * q^34 + 19200 * q^38 - 12208 * q^40 - 2476 * q^41 + 18396 * q^42 + 75560 * q^44 - 49584 * q^46 - 8712 * q^48 - 350772 * q^49 - 52408 * q^50 - 83908 * q^52 + 151824 * q^55 + 86292 * q^56 - 51552 * q^57 - 16204 * q^58 + 127296 * q^60 - 35920 * q^62 - 65688 * q^64 - 104588 * q^65 - 165384 * q^66 + 24032 * q^68 - 193488 * q^70 + 287680 * q^71 + 54776 * q^73 - 50472 * q^74 - 285628 * q^76 + 91944 * q^78 + 499280 * q^79 - 304364 * q^80 - 918540 * q^81 + 114692 * q^82 + 614400 * q^86 + 181656 * q^87 - 86412 * q^88 - 351160 * q^89 + 46008 * q^90 - 400328 * q^92 - 159144 * q^94 + 204760 * q^95 + 250200 * q^96 + 234496 * q^97 + 491648 * q^98

Decomposition of \(S_{6}^{\mathrm{new}}(312, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)