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

• Label: 2370.4.r
• Level: $2370$
• Weight: $4$
• Character orbit: 2370.r
• Rep. character: $\chi_{2370}(529,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $480$
• Sturm bound: $1920$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2370.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(1920\)

Dimensions

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

	Total	New	Old
Modular forms	2896	480	2416
Cusp forms	2864	480	2384
Eisenstein series	32	0	32

Trace form

480 * q + 960 * q^4 + 24 * q^6 + 2160 * q^9 + 24 * q^10 + 84 * q^15 - 3840 * q^16 - 144 * q^19 - 192 * q^21 - 96 * q^24 + 214 * q^25 + 64 * q^29 + 672 * q^31 - 400 * q^34 - 1288 * q^35 - 8640 * q^36 - 684 * q^39 + 48 * q^40 + 768 * q^41 + 144 * q^46 + 12900 * q^49 + 112 * q^50 - 672 * q^51 - 216 * q^54 - 510 * q^55 + 1088 * q^59 + 168 * q^60 - 1072 * q^61 - 30720 * q^64 + 2728 * q^65 + 744 * q^66 + 2592 * q^69 - 1364 * q^70 - 368 * q^71 - 464 * q^74 - 1200 * q^75 + 576 * q^76 - 4272 * q^79 - 19440 * q^81 - 384 * q^84 + 1080 * q^85 + 1168 * q^86 + 2704 * q^89 + 108 * q^90 - 12016 * q^91 + 9152 * q^94 + 8216 * q^95 - 768 * q^96

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

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