Space of modular forms of level 312, weight 4, and Character 312.bn

• Label: 312.4.bn
• Level: $312$
• Weight: $4$
• Character orbit: 312.bn
• Rep. character: $\chi_{312}(35,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $328$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.bn (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 312 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(312, [\chi])\).

	Total	New	Old
Modular forms	344	344	0
Cusp forms	328	328	0
Eisenstein series	16	16	0

Trace form

328 * q - 2 * q^3 - 2 * q^4 - 32 * q^6 - 2 * q^9 + 18 * q^10 - 28 * q^12 - 38 * q^16 + 352 * q^18 - 4 * q^19 - 16 * q^22 + 210 * q^24 + 7384 * q^25 + 256 * q^27 - 240 * q^28 - 96 * q^30 - 110 * q^33 + 140 * q^34 + 118 * q^36 - 876 * q^40 - 584 * q^42 - 436 * q^43 - 480 * q^46 - 72 * q^48 + 6496 * q^49 - 116 * q^51 + 1752 * q^52 + 702 * q^54 + 100 * q^57 + 606 * q^58 - 972 * q^60 - 2132 * q^64 + 2308 * q^66 - 4 * q^67 - 4440 * q^70 - 866 * q^72 - 448 * q^73 - 306 * q^75 + 1364 * q^76 - 3832 * q^78 - 2 * q^81 + 1262 * q^82 + 1698 * q^84 + 4748 * q^88 + 4296 * q^90 - 3180 * q^91 - 3480 * q^94 - 10360 * q^96 - 796 * q^97 + 7700 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(312, [\chi])\) into newform subspaces

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