Space of modular forms of level 1862, weight 2, and Character 1862.k

• Label: 1862.2.k
• Level: $1862$
• Weight: $2$
• Character orbit: 1862.k
• Rep. character: $\chi_{1862}(411,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $136$
• Sturm bound: $560$

Defining parameters

Level:	\( N \)	\(=\)	\( 1862 = 2 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1862.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 133 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1862, [\chi])\).

	Total	New	Old
Modular forms	592	136	456
Cusp forms	528	136	392
Eisenstein series	64	0	64

Trace form

136 * q - 136 * q^4 - 72 * q^9 + 6 * q^13 - 42 * q^15 + 136 * q^16 - 24 * q^17 + 12 * q^19 - 30 * q^22 - 18 * q^23 - 148 * q^25 + 12 * q^26 + 30 * q^29 + 16 * q^30 + 6 * q^31 + 12 * q^34 + 72 * q^36 - 42 * q^37 + 18 * q^38 - 26 * q^39 - 6 * q^41 - 44 * q^43 + 90 * q^45 - 6 * q^46 - 12 * q^47 - 6 * q^52 + 6 * q^55 - 58 * q^57 - 4 * q^58 + 42 * q^59 + 42 * q^60 + 12 * q^61 - 136 * q^64 - 48 * q^65 + 24 * q^68 - 24 * q^69 - 114 * q^71 - 78 * q^73 - 16 * q^74 - 66 * q^75 - 12 * q^76 + 48 * q^78 - 68 * q^81 + 8 * q^85 - 24 * q^86 + 48 * q^87 + 30 * q^88 + 18 * q^92 + 48 * q^93 + 30 * q^94 + 30 * q^95 + 30 * q^97 - 22 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(1862, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1862, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1862, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(931, [\chi])\)\(^{\oplus 2}\)