Space of modular forms of level 3822, weight 2, and Character 3822.l

• Label: 3822.2.l
• Level: $3822$
• Weight: $2$
• Character orbit: 3822.l
• Rep. character: $\chi_{3822}(295,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $188$
• Sturm bound: $1568$

Defining parameters

Level:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.l (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(1568\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3822, [\chi])\).

	Total	New	Old
Modular forms	1632	188	1444
Cusp forms	1504	188	1316
Eisenstein series	128	0	128

Trace form

188 * q + 2 * q^2 - 94 * q^4 + 4 * q^5 - 4 * q^8 - 94 * q^9 - 6 * q^10 - 2 * q^13 - 4 * q^15 - 94 * q^16 - 10 * q^17 - 4 * q^18 + 16 * q^19 - 2 * q^20 - 16 * q^23 + 200 * q^25 + 18 * q^26 - 18 * q^29 + 4 * q^30 + 16 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 - 94 * q^36 - 50 * q^37 + 16 * q^38 + 24 * q^39 + 12 * q^40 + 6 * q^41 - 28 * q^43 - 2 * q^45 - 8 * q^46 - 32 * q^47 - 24 * q^50 + 4 * q^52 + 100 * q^53 - 8 * q^55 + 48 * q^57 - 46 * q^58 - 8 * q^59 + 8 * q^60 - 46 * q^61 + 8 * q^62 + 188 * q^64 - 66 * q^65 + 24 * q^66 + 56 * q^67 - 10 * q^68 - 20 * q^69 - 32 * q^71 + 2 * q^72 - 36 * q^73 - 34 * q^74 + 8 * q^75 + 16 * q^76 - 48 * q^79 - 2 * q^80 - 94 * q^81 + 2 * q^82 + 64 * q^83 + 62 * q^85 + 16 * q^86 + 12 * q^87 + 20 * q^89 + 12 * q^90 + 32 * q^92 + 56 * q^93 - 8 * q^94 + 56 * q^95 + 4 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(3822, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3822, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)