Space of modular forms of level 2370, weight 2, and Character 2370.bn

• Label: 2370.2.bn
• Level: $2370$
• Weight: $2$
• Character orbit: 2370.bn
• Rep. character: $\chi_{2370}(19,\cdot)$
• Character field: $\Q(\zeta_{78})$
• Dimension: $1920$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2370.bn (of order \(78\) and degree \(24\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{78})\)
Sturm bound:			\(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2370, [\chi])\).

	Total	New	Old
Modular forms	11712	1920	9792
Cusp forms	11328	1920	9408
Eisenstein series	384	0	384

Trace form

1920 * q - 80 * q^4 + 4 * q^6 - 80 * q^9 - 4 * q^10 - 4 * q^15 + 80 * q^16 - 8 * q^19 - 16 * q^21 + 48 * q^24 - 12 * q^25 + 16 * q^29 - 68 * q^31 - 8 * q^34 - 16 * q^35 + 80 * q^36 + 12 * q^39 - 2 * q^40 + 48 * q^41 - 8 * q^46 - 68 * q^49 - 112 * q^50 - 16 * q^51 - 4 * q^54 + 14 * q^55 + 264 * q^59 - 2 * q^60 - 64 * q^61 + 160 * q^64 + 80 * q^65 - 84 * q^66 + 208 * q^69 + 90 * q^70 - 192 * q^71 + 200 * q^74 + 192 * q^75 - 200 * q^76 + 48 * q^79 + 80 * q^81 + 200 * q^84 + 224 * q^85 - 216 * q^86 + 224 * q^89 + 50 * q^90 - 504 * q^91 + 232 * q^94 + 264 * q^95 - 8 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(2370, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2370, [\chi])\) into lower level spaces

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