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

• Label: 2370.4.bn
• Level: $2370$
• Weight: $4$
• Character orbit: 2370.bn
• Rep. character: $\chi_{2370}(19,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $5760$
• Sturm bound: $1920$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2370.bn (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{78})\)
Sturm bound:			\(1920\)

Dimensions

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

	Total	New	Old
Modular forms	34752	5760	28992
Cusp forms	34368	5760	28608
Eisenstein series	384	0	384

Trace form

5760 * 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 - 1152 * q^24 + 332 * q^25 - 64 * q^29 - 4260 * 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 - 1568 * q^50 + 672 * q^51 + 216 * q^54 + 510 * q^55 + 7440 * q^59 - 168 * q^60 + 1072 * q^61 + 30720 * q^64 + 18904 * q^65 - 8856 * q^66 - 96 * q^69 + 2612 * q^70 + 4944 * q^71 - 11600 * q^74 - 12528 * q^75 + 14400 * q^76 + 4272 * q^79 + 19440 * q^81 - 9600 * q^84 - 8568 * q^85 + 3408 * q^86 + 3952 * q^89 + 2700 * q^90 - 46016 * q^91 + 7696 * q^94 + 32136 * 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

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