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

• Label: 312.4.t
• Level: $312$
• Weight: $4$
• Character orbit: 312.t
• Rep. character: $\chi_{312}(187,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $168$
• Sturm bound: $224$

Defining parameters

Level:	\( N \)	\(=\)	\( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	312.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(i)\)
Sturm bound:			\(224\)

Dimensions

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

	Total	New	Old
Modular forms	344	168	176
Cusp forms	328	168	160
Eisenstein series	16	0	16

Trace form

168 * q + 1512 * q^9 - 416 * q^14 - 72 * q^16 + 300 * q^20 - 736 * q^22 - 180 * q^24 - 500 * q^26 + 416 * q^28 - 820 * q^32 + 1072 * q^34 + 912 * q^40 - 472 * q^41 - 936 * q^42 - 1332 * q^44 + 1840 * q^46 + 1248 * q^48 + 3184 * q^50 + 968 * q^52 + 336 * q^57 - 1224 * q^58 + 2752 * q^59 - 1644 * q^60 + 1048 * q^65 - 1272 * q^66 - 1032 * q^68 - 3392 * q^70 + 1912 * q^73 - 600 * q^74 - 3056 * q^76 + 1308 * q^78 - 3236 * q^80 + 13608 * q^81 + 5360 * q^83 + 2064 * q^86 + 440 * q^89 - 6992 * q^91 - 5856 * q^92 - 6064 * q^94 + 2280 * q^96 - 232 * q^97 - 4240 * q^98

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

\( S_{4}^{\mathrm{old}}(312, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)