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

• Label: 1862.2.bm
• Level: $1862$
• Weight: $2$
• Character orbit: 1862.bm
• Rep. character: $\chi_{1862}(239,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $1152$
• Sturm bound: $560$

Defining parameters

Level:	$N$	$=$	$1862 = 2 \cdot 7^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1862.bm (of order $21$ and degree $12$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$931$
Character field:			$\Q(\zeta_{21})$
Sturm bound:			$560$

Dimensions

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

	Total	New	Old
Modular forms	3408	1152	2256
Cusp forms	3312	1152	2160
Eisenstein series	96	0	96

Trace form

1152 * q + 4 * q^3 + 96 * q^4 + 4 * q^5 + 4 * q^7 + 104 * q^9 + 4 * q^10 + 28 * q^11 - 8 * q^12 - 4 * q^13 + 2 * q^14 - 12 * q^15 + 96 * q^16 - 26 * q^17 - 28 * q^19 + 20 * q^20 + 6 * q^21 - 4 * q^22 + 4 * q^23 + 116 * q^25 + 40 * q^26 - 8 * q^27 - 2 * q^28 - 4 * q^29 + 32 * q^31 + 8 * q^33 + 6 * q^35 + 104 * q^36 - 112 * q^37 - 2 * q^38 - 124 * q^39 + 4 * q^40 + 12 * q^41 - 108 * q^42 - 4 * q^43 + 14 * q^44 - 28 * q^45 + 8 * q^46 - 26 * q^47 - 24 * q^48 - 48 * q^50 + 24 * q^52 - 4 * q^53 + 12 * q^54 - 46 * q^55 - 32 * q^56 - 90 * q^57 - 40 * q^58 - 36 * q^59 - 12 * q^60 + 70 * q^61 + 10 * q^62 + 114 * q^63 - 192 * q^64 - 16 * q^65 - 16 * q^66 - 28 * q^67 + 24 * q^68 + 24 * q^69 - 12 * q^70 + 30 * q^71 + 32 * q^73 + 22 * q^74 - 52 * q^75 + 8 * q^76 + 44 * q^77 + 40 * q^78 + 4 * q^80 + 96 * q^81 + 16 * q^82 - 108 * q^83 + 156 * q^84 + 64 * q^85 - 88 * q^87 - 20 * q^88 + 82 * q^89 + 52 * q^90 + 62 * q^91 + 4 * q^92 + 32 * q^93 + 208 * q^94 - 16 * q^95 - 20 * q^97 - 16 * q^98 + 172 * 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}}(931, [\chi])$$^{\oplus 2}$