Space of modular forms of level 1152, weight 4, and Character 1152.v

• Label: 1152.4.v
• Level: $1152$
• Weight: $4$
• Character orbit: 1152.v
• Rep. character: $\chi_{1152}(145,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $236$
• Sturm bound: $768$

Defining parameters

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1152.v (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Sturm bound:			\(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1152, [\chi])\).

	Total	New	Old
Modular forms	2368	244	2124
Cusp forms	2240	236	2004
Eisenstein series	128	8	120

Trace form

236 * q + 4 * q^5 + 4 * q^7 - 4 * q^11 - 4 * q^13 + 4 * q^19 - 332 * q^23 - 4 * q^25 + 4 * q^29 + 752 * q^31 + 452 * q^35 - 4 * q^37 + 4 * q^41 - 804 * q^43 + 756 * q^53 - 284 * q^55 - 1380 * q^59 + 1820 * q^61 + 8 * q^65 - 404 * q^67 - 228 * q^71 - 4 * q^73 + 1908 * q^77 + 2436 * q^83 + 496 * q^85 + 4 * q^89 - 3596 * q^91 - 6088 * q^95 - 8 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1152, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)