Space of modular forms of level 2366, weight 2, and Character 2366.g

• Label: 2366.2.g
• Level: $2366$
• Weight: $2$
• Character orbit: 2366.g
• Rep. character: $\chi_{2366}(1205,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $156$
• Sturm bound: $728$

Defining parameters

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2366, [\chi])\).

	Total	New	Old
Modular forms	784	156	628
Cusp forms	672	156	516
Eisenstein series	112	0	112

Trace form

156 * q - 2 * q^2 - 78 * q^4 - 4 * q^5 + 4 * q^8 - 78 * q^9 + 6 * q^10 - 4 * q^11 + 8 * q^14 + 4 * q^15 - 78 * q^16 + 6 * q^17 + 12 * q^18 - 16 * q^19 + 2 * q^20 - 8 * q^21 - 4 * q^22 + 4 * q^23 + 152 * q^25 - 24 * q^27 + 2 * q^29 + 8 * q^30 - 8 * q^31 - 2 * q^32 + 32 * q^33 + 12 * q^34 - 12 * q^35 - 78 * q^36 + 6 * q^37 - 32 * q^38 - 12 * q^40 + 14 * q^41 - 4 * q^42 + 8 * q^44 - 26 * q^45 + 12 * q^46 + 16 * q^47 - 78 * q^49 - 4 * q^50 - 56 * q^51 + 28 * q^53 - 12 * q^54 + 12 * q^55 - 4 * q^56 + 24 * q^57 + 2 * q^58 + 16 * q^59 - 8 * q^60 + 18 * q^61 + 12 * q^62 + 4 * q^63 + 156 * q^64 + 48 * q^66 + 12 * q^67 + 6 * q^68 - 20 * q^69 - 6 * q^72 + 36 * q^73 - 46 * q^74 + 40 * q^75 - 16 * q^76 - 16 * q^79 + 2 * q^80 - 130 * q^81 + 2 * q^82 + 24 * q^83 + 4 * q^84 + 34 * q^85 - 24 * q^86 - 28 * q^87 - 4 * q^88 - 28 * q^89 - 20 * q^90 - 8 * q^92 + 40 * q^93 - 8 * q^94 - 12 * q^95 - 12 * q^97 - 2 * q^98 - 40 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2366, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2366, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2366, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1183, [\chi])\)\(^{\oplus 2}\)