Space of modular forms of level 3681, weight 2, and Character 3681.ch

• Label: 3681.2.ch
• Level: $3681$
• Weight: $2$
• Character orbit: 3681.ch
• Rep. character: $\chi_{3681}(193,\cdot)$
• Character field: $\Q(\zeta_{102})$
• Dimension: $13056$
• Sturm bound: $820$

Defining parameters

Level:	$N$	$=$	$3681 = 3^{2} \cdot 409$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3681.ch (of order $102$ and degree $32$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$3681$
Character field:			$\Q(\zeta_{102})$
Sturm bound:			$820$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3681, [\chi])$.

	Total	New	Old
Modular forms	13184	13184	0
Cusp forms	13056	13056	0
Eisenstein series	128	128	0

Trace form

13056 * q - 13 * q^2 - 32 * q^3 + 391 * q^4 - 19 * q^5 + 34 * q^6 - 92 * q^8 - 40 * q^9 - 68 * q^10 + 62 * q^12 - 17 * q^13 - 85 * q^14 - 36 * q^15 + 391 * q^16 - 32 * q^17 - 30 * q^18 - 68 * q^19 - 53 * q^20 - 85 * q^21 - 17 * q^22 - 9 * q^23 - 73 * q^24 + 385 * q^25 - 68 * q^26 - 8 * q^27 - 204 * q^28 - 17 * q^29 - 42 * q^30 - 91 * q^32 - 34 * q^33 + 7 * q^34 - 238 * q^35 - 282 * q^36 - 68 * q^37 + 68 * q^39 + 7 * q^40 - 96 * q^41 + 136 * q^42 - 17 * q^43 - 68 * q^44 + 10 * q^45 - 116 * q^46 - 17 * q^47 - 50 * q^48 + 6314 * q^49 - 41 * q^50 + 44 * q^51 - 17 * q^52 - 552 * q^53 - 110 * q^54 - 272 * q^55 + 102 * q^56 - 34 * q^57 - 17 * q^58 - 17 * q^59 + 62 * q^60 - 17 * q^61 - 136 * q^62 - 34 * q^63 - 1088 * q^64 - 17 * q^65 - 17 * q^67 - q^68 - 112 * q^69 + 204 * q^70 + 28 * q^71 + 88 * q^72 - 68 * q^73 - 17 * q^74 - 14 * q^75 - 85 * q^76 - 258 * q^77 + 68 * q^78 - 17 * q^79 - 360 * q^80 - 124 * q^81 - 140 * q^82 - 35 * q^83 + 153 * q^84 + 19 * q^85 - 17 * q^86 - 476 * q^87 - 17 * q^88 + 24 * q^89 - 177 * q^90 - 282 * q^91 - 45 * q^92 - 85 * q^93 - 17 * q^94 - 17 * q^95 - 59 * q^96 - 17 * q^97 - 736 * q^98 + 374 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(3681, [\chi])$ into newform subspaces

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