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

• Label: 3681.2.da
• Level: $3681$
• Weight: $2$
• Character orbit: 3681.da
• Rep. character: $\chi_{3681}(110,\cdot)$
• Character field: $\Q(\zeta_{408})$
• Dimension: $52224$
• Sturm bound: $820$

Defining parameters

Level:	$N$	$=$	$3681 = 3^{2} \cdot 409$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3681.da (of order $408$ and degree $128$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$3681$
Character field:			$\Q(\zeta_{408})$
Sturm bound:			$820$

Dimensions

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

	Total	New	Old
Modular forms	52736	52736	0
Cusp forms	52224	52224	0
Eisenstein series	512	512	0

Trace form

52224 * q - 192 * q^2 - 124 * q^3 - 68 * q^4 - 180 * q^5 - 120 * q^6 - 64 * q^7 - 24 * q^8 - 160 * q^9 - 240 * q^10 - 192 * q^11 - 120 * q^12 - 64 * q^13 - 168 * q^14 - 116 * q^15 + 3156 * q^16 - 100 * q^18 - 256 * q^19 - 192 * q^20 - 96 * q^21 - 64 * q^22 - 192 * q^23 - 172 * q^24 - 1660 * q^25 - 136 * q^27 - 240 * q^28 - 192 * q^29 - 108 * q^30 - 64 * q^31 - 240 * q^32 - 180 * q^33 - 84 * q^34 - 60 * q^35 - 136 * q^36 - 256 * q^37 - 192 * q^38 + 256 * q^39 - 116 * q^40 - 276 * q^41 - 196 * q^42 - 40 * q^43 + 84 * q^44 - 64 * q^45 - 248 * q^46 - 192 * q^47 - 248 * q^48 - 24 * q^49 - 132 * q^50 - 136 * q^51 - 108 * q^52 + 48 * q^53 - 192 * q^54 - 600 * q^55 - 192 * q^56 - 164 * q^57 - 100 * q^58 - 192 * q^59 - 148 * q^60 - 16 * q^61 + 72 * q^62 + 8 * q^63 - 272 * q^64 - 192 * q^65 - 76 * q^66 - 76 * q^67 - 252 * q^68 + 672 * q^69 - 24 * q^70 - 208 * q^72 - 200 * q^73 - 108 * q^74 - 36 * q^75 - 136 * q^76 - 816 * q^77 - 484 * q^78 - 64 * q^79 + 192 * q^80 - 152 * q^81 - 312 * q^82 - 180 * q^83 - 1000 * q^84 - 52 * q^85 - 192 * q^86 - 320 * q^87 - 92 * q^88 - 140 * q^90 - 248 * q^91 - 192 * q^92 - 212 * q^93 - 88 * q^94 - 132 * q^95 - 172 * q^96 - 16 * q^97 + 144 * q^98 - 152 * 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.