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

• Label: 2370.2.bd
• Level: $2370$
• Weight: $2$
• Character orbit: 2370.bd
• Rep. character: $\chi_{2370}(259,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $960$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2370.bd (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 395 \)
Character field:			\(\Q(\zeta_{26})\)
Sturm bound:			\(960\)

Dimensions

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

	Total	New	Old
Modular forms	5856	960	4896
Cusp forms	5664	960	4704
Eisenstein series	192	0	192

Trace form

960 * q + 80 * q^4 - 4 * q^6 + 80 * q^9 + 4 * q^10 + 4 * q^15 - 80 * q^16 - 16 * q^19 + 16 * q^21 - 48 * q^24 + 6 * q^25 + 32 * q^29 + 68 * q^31 + 8 * q^34 - 8 * q^35 - 80 * q^36 - 24 * q^39 - 4 * q^40 - 48 * q^41 + 8 * q^46 + 56 * q^49 + 88 * q^50 + 16 * q^51 + 4 * q^54 + 16 * q^55 - 144 * q^59 - 4 * q^60 - 8 * q^61 + 80 * q^64 + 112 * q^65 - 60 * q^66 + 104 * q^69 - 18 * q^70 - 72 * q^71 + 88 * q^74 + 120 * q^75 - 88 * q^76 - 80 * q^81 + 88 * q^84 + 64 * q^85 - 120 * q^86 + 88 * q^89 + 22 * q^90 + 192 * q^91 + 92 * q^94 + 48 * q^95 - 4 * 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

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