Space of modular forms of level 2370, weight 4, and Character 2370.u

• Label: 2370.4.u
• Level: $2370$
• Weight: $4$
• Character orbit: 2370.u
• Rep. character: $\chi_{2370}(103,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $960$
• Sturm bound: $1920$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2370.u (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(1920\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2370, [\chi])\).

	Total	New	Old
Modular forms	5792	960	4832
Cusp forms	5728	960	4768
Eisenstein series	64	0	64

Trace form

960 * q - 36 * q^7 + 48 * q^10 + 7680 * q^16 + 384 * q^21 + 336 * q^22 - 352 * q^23 - 144 * q^28 + 792 * q^31 + 17280 * q^36 - 2016 * q^37 + 1408 * q^38 - 408 * q^42 + 1488 * q^43 - 288 * q^46 - 1344 * q^51 + 3744 * q^53 - 804 * q^55 - 2784 * q^62 - 324 * q^63 - 5040 * q^65 + 1872 * q^66 + 3168 * q^67 + 2592 * q^70 - 1656 * q^73 + 288 * q^75 - 1152 * q^76 - 6624 * q^77 + 38880 * q^81 + 864 * q^82 + 3952 * q^83 + 1728 * q^85 + 2880 * q^86 - 1896 * q^87 + 672 * q^88 - 1408 * q^92 + 3520 * q^95 + 1272 * q^97 + 96 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(2370, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2370, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2370, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(790, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1185, [\chi])\)\(^{\oplus 2}\)