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

• Label: 312.4.j
• Level: $312$
• Weight: $4$
• Character orbit: 312.j
• Rep. character: $\chi_{312}(131,\cdot)$
• Character field: $\Q$
• Dimension: $144$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Sturm bound:			\(224\)

Dimensions

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

	Total	New	Old
Modular forms	172	144	28
Cusp forms	164	144	20
Eisenstein series	8	0	8

Trace form

144 * q - 12 * q^4 - 24 * q^10 + 110 * q^12 + 336 * q^16 - 168 * q^18 + 48 * q^19 - 60 * q^22 - 236 * q^24 + 3600 * q^25 - 768 * q^28 + 846 * q^30 + 232 * q^33 + 1416 * q^34 + 570 * q^36 + 888 * q^40 - 2002 * q^42 - 432 * q^43 - 1776 * q^46 - 1538 * q^48 - 7056 * q^49 - 1400 * q^51 - 468 * q^52 + 2524 * q^54 - 344 * q^57 + 2784 * q^58 + 5496 * q^60 + 3108 * q^64 - 1304 * q^66 + 3264 * q^67 - 5976 * q^70 - 2328 * q^72 + 3304 * q^75 - 5256 * q^76 + 910 * q^78 - 312 * q^81 + 1188 * q^82 + 4956 * q^84 + 7164 * q^88 - 7098 * q^90 - 2664 * q^94 - 7972 * q^96 - 1488 * q^97

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)