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

• Label: 2370.2.y
• Level: $2370$
• Weight: $2$
• Character orbit: 2370.y
• Rep. character: $\chi_{2370}(301,\cdot)$
• Character field: $\Q(\zeta_{13})$
• Dimension: $672$
• Sturm bound: $960$

Defining parameters

Level:	\( N \)	\(=\)	\( 2370 = 2 \cdot 3 \cdot 5 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2370.y (of order \(13\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{13})\)
Sturm bound:			\(960\)

Dimensions

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

	Total	New	Old
Modular forms	5856	672	5184
Cusp forms	5664	672	4992
Eisenstein series	192	0	192

Trace form

672 * q - 4 * q^3 - 56 * q^4 - 8 * q^7 - 56 * q^9 - 16 * q^11 - 4 * q^12 - 24 * q^13 - 56 * q^16 - 16 * q^17 - 8 * q^19 - 8 * q^21 - 16 * q^23 - 56 * q^25 - 4 * q^27 - 8 * q^28 - 4 * q^30 - 32 * q^31 - 8 * q^33 - 24 * q^34 - 56 * q^36 + 56 * q^37 - 16 * q^38 - 32 * q^39 - 32 * q^41 + 88 * q^42 - 32 * q^43 - 16 * q^44 - 24 * q^46 + 160 * q^47 - 4 * q^48 + 64 * q^49 - 16 * q^51 - 24 * q^52 - 64 * q^53 - 24 * q^55 - 32 * q^57 - 40 * q^58 - 80 * q^59 - 56 * q^61 - 32 * q^62 + 44 * q^63 - 56 * q^64 - 16 * q^65 + 28 * q^66 + 52 * q^67 + 88 * q^68 + 56 * q^69 - 8 * q^70 + 72 * q^71 + 48 * q^73 + 72 * q^74 - 4 * q^75 + 44 * q^76 + 232 * q^77 + 96 * q^78 - 88 * q^79 - 56 * q^81 + 40 * q^82 + 200 * q^83 + 44 * q^84 - 8 * q^85 + 24 * q^86 + 72 * q^87 - 40 * q^89 - 24 * q^91 + 88 * q^92 + 284 * q^93 - 20 * q^94 - 48 * q^95 + 108 * q^97 - 32 * q^98 - 16 * q^99

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

\( S_{2}^{\mathrm{old}}(2370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(158, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(237, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(395, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(474, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(790, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1185, [\chi])\)\(^{\oplus 2}\)