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

• Label: 312.6.bt
• Level: $312$
• Weight: $6$
• Character orbit: 312.bt
• Rep. character: $\chi_{312}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $560$
• Sturm bound: $336$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	312.bt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(336\)

Dimensions

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

	Total	New	Old
Modular forms	1136	560	576
Cusp forms	1104	560	544
Eisenstein series	32	0	32

Trace form

560 * q - 22680 * q^9 - 4960 * q^14 - 2552 * q^16 + 22020 * q^20 - 3372 * q^22 - 108 * q^24 + 23960 * q^26 - 12652 * q^28 + 17560 * q^32 - 28352 * q^34 + 31704 * q^40 + 9904 * q^41 + 22572 * q^42 + 94920 * q^44 + 110044 * q^46 - 17424 * q^48 + 87792 * q^49 - 149092 * q^50 - 17704 * q^52 + 47412 * q^56 + 51552 * q^57 + 11768 * q^58 + 57920 * q^59 + 127296 * q^60 + 241260 * q^62 + 70736 * q^65 - 166896 * q^66 - 3576 * q^68 - 41272 * q^70 + 54776 * q^73 + 72024 * q^74 + 331004 * q^76 - 70236 * q^78 - 320764 * q^80 - 1837080 * q^81 - 71940 * q^82 + 252880 * q^83 + 614400 * q^86 - 750108 * q^88 + 351160 * q^89 + 1117648 * q^91 - 1083576 * q^92 - 387836 * q^94 + 250200 * q^96 + 308184 * q^97 - 477308 * 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

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