Space of modular forms of level 1185, weight 4, and Character 1185.v

• Label: 1185.4.v
• Level: $1185$
• Weight: $4$
• Character orbit: 1185.v
• Rep. character: $\chi_{1185}(103,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $960$
• Sturm bound: $640$

Defining parameters

Level:	\( N \)	\(=\)	\( 1185 = 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1185.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1185, [\chi])\).

	Total	New	Old
Modular forms	1936	960	976
Cusp forms	1904	960	944
Eisenstein series	32	0	32

Trace form

960 * q + 36 * q^7 - 336 * q^10 + 8136 * q^16 + 380 * q^20 - 192 * q^21 - 680 * q^22 + 176 * q^23 + 432 * q^28 - 1224 * q^30 - 240 * q^31 - 340 * q^32 + 17496 * q^36 + 1008 * q^37 - 1408 * q^38 + 1468 * q^40 + 408 * q^42 - 1872 * q^43 + 8352 * q^46 + 576 * q^48 + 344 * q^50 - 72 * q^51 - 1224 * q^52 - 1872 * q^53 + 684 * q^55 + 6128 * q^62 + 324 * q^63 + 3696 * q^65 - 1872 * q^66 - 2592 * q^67 + 8844 * q^68 - 2592 * q^70 + 2376 * q^73 - 144 * q^75 + 5864 * q^76 + 3312 * q^77 - 416 * q^80 + 38880 * q^81 + 7896 * q^82 + 1608 * q^83 - 864 * q^85 + 5520 * q^86 + 1896 * q^87 - 3780 * q^88 + 2700 * q^92 - 3656 * q^95 + 6456 * q^97 - 4516 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(1185, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1185, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1185, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 2}\)