Space of modular forms of level 3721, weight 2, and Character 3721.c

• Label: 3721.2.c
• Level: $3721$
• Weight: $2$
• Character orbit: 3721.c
• Rep. character: $\chi_{3721}(1660,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $552$
• Sturm bound: $630$

Defining parameters

Level:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q(\zeta_{3})\)
Sturm bound:			\(630\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3721, [\chi])\).

	Total	New	Old
Modular forms	692	668	24
Cusp forms	568	552	16
Eisenstein series	124	116	8

Trace form

552 * q + 6 * q^3 - 250 * q^4 + 2 * q^5 + q^6 + q^7 + 6 * q^8 + 438 * q^9 + 2 * q^11 + 7 * q^12 - 5 * q^13 - 4 * q^14 - 8 * q^15 - 194 * q^16 - 4 * q^17 + 10 * q^18 - q^19 - 14 * q^20 + 2 * q^21 + q^22 + 8 * q^23 - 10 * q^24 - 152 * q^25 - 9 * q^26 + 30 * q^27 + 4 * q^28 + 16 * q^29 - 6 * q^30 - 11 * q^31 + 4 * q^32 - 10 * q^33 + 28 * q^34 - 13 * q^35 - 145 * q^36 - 4 * q^37 - 24 * q^38 - 8 * q^39 - 15 * q^40 - 4 * q^41 + 3 * q^42 - 10 * q^43 + 14 * q^44 + 27 * q^45 - 7 * q^46 - 20 * q^48 - 119 * q^49 + 14 * q^50 + 16 * q^51 + 24 * q^52 - 38 * q^53 - 26 * q^54 + 20 * q^55 + 8 * q^56 + 12 * q^57 + 74 * q^58 - q^59 - 20 * q^60 - 122 * q^62 - 18 * q^63 + 166 * q^64 - 2 * q^65 - 4 * q^66 + 17 * q^67 + 27 * q^68 + 38 * q^69 + 16 * q^70 + 3 * q^71 + 38 * q^72 + 24 * q^73 - 20 * q^74 - 29 * q^75 - 23 * q^76 - 17 * q^77 - 13 * q^78 + 16 * q^79 - 16 * q^80 + 8 * q^81 - 6 * q^82 - 16 * q^83 + 10 * q^84 - 24 * q^85 + 18 * q^86 - 23 * q^87 + 36 * q^88 - 8 * q^89 + 25 * q^90 - 33 * q^92 - 8 * q^93 - 74 * q^94 + 82 * q^95 - 26 * q^96 - 19 * q^97 + 2 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(3721, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3721, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3721, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(61, [\chi])\)\(^{\oplus 2}\)