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

• Label: 3681.2.ct
• Level: $3681$
• Weight: $2$
• Character orbit: 3681.ct
• Rep. character: $\chi_{3681}(115,\cdot)$
• Character field: $\Q(\zeta_{204})$
• Dimension: $26112$
• Sturm bound: $820$

Defining parameters

Level:	$N$	$=$	$3681 = 3^{2} \cdot 409$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3681.ct (of order $204$ and degree $64$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$3681$
Character field:			$\Q(\zeta_{204})$
Sturm bound:			$820$

Dimensions

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

	Total	New	Old
Modular forms	26368	26368	0
Cusp forms	26112	26112	0
Eisenstein series	256	256	0

Trace form

26112 * q - 34 * q^2 - 68 * q^3 + 1594 * q^4 - 22 * q^5 - 64 * q^6 - 36 * q^7 - 136 * q^8 - 68 * q^9 - 136 * q^10 - 28 * q^11 - 56 * q^12 - 30 * q^13 - 44 * q^14 - 80 * q^15 - 1646 * q^16 - 116 * q^17 - 62 * q^18 - 114 * q^19 - 52 * q^20 - 62 * q^21 - 54 * q^22 - 28 * q^23 - 80 * q^24 + 770 * q^25 - 152 * q^26 - 68 * q^27 - 108 * q^28 - 44 * q^29 - 58 * q^30 - 24 * q^31 + 374 * q^32 - 54 * q^33 - 28 * q^34 - 138 * q^35 - 256 * q^36 - 126 * q^37 + 904 * q^38 + 126 * q^39 - 34 * q^40 + 204 * q^41 - 74 * q^42 - 36 * q^43 - 114 * q^44 - 98 * q^45 - 164 * q^46 - 52 * q^47 - 80 * q^48 - 126 * q^49 - 22 * q^50 - 98 * q^51 + 6 * q^52 - 456 * q^53 - 18 * q^54 + 44 * q^55 - 70 * q^56 - 118 * q^57 - 18 * q^58 - 26 * q^59 - 38 * q^60 - 42 * q^61 - 206 * q^62 - 88 * q^63 + 1752 * q^64 - 92 * q^65 - 34 * q^66 - 12 * q^67 - 94 * q^68 - 462 * q^69 - 238 * q^70 - 60 * q^71 - 122 * q^72 - 64 * q^73 - 22 * q^74 - 8 * q^75 - 72 * q^76 - 136 * q^77 + 12 * q^78 - 18 * q^79 - 196 * q^80 - 76 * q^81 - 92 * q^82 + 18 * q^83 - 806 * q^84 - 46 * q^85 - 86 * q^86 - 200 * q^87 - 2 * q^88 - 196 * q^89 - 212 * q^90 - 148 * q^91 - 58 * q^92 + 14 * q^93 - 54 * q^94 - 22 * q^95 - 104 * q^96 - 24 * q^97 - 60 * q^98 + 62 * 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.