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

• Label: 3721.2.k
• Level: $3721$
• Weight: $2$
• Character orbit: 3721.k
• Rep. character: $\chi_{3721}(432,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $2200$
• Sturm bound: $630$

Defining parameters

Level:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.k (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 61 \)
Character field:			\(\Q(\zeta_{30})\)
Sturm bound:			\(630\)

Dimensions

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

	Total	New	Old
Modular forms	2776	2664	112
Cusp forms	2280	2200	80
Eisenstein series	496	464	32

Trace form

2200 * q + 7 * q^2 + 4 * q^3 - 231 * q^4 + 18 * q^5 - 15 * q^6 + 11 * q^7 + 10 * q^8 - 416 * q^9 + 13 * q^10 - 41 * q^12 + 14 * q^13 - 15 * q^14 - 10 * q^15 + 205 * q^16 - 6 * q^17 - 46 * q^18 + 35 * q^19 + 14 * q^20 + 33 * q^21 + 19 * q^22 - 30 * q^23 - 5 * q^24 + 157 * q^25 + 4 * q^26 - 11 * q^27 - 33 * q^29 - 21 * q^31 + 54 * q^32 - 5 * q^33 - 38 * q^34 - 14 * q^35 - 74 * q^36 + 10 * q^37 - 21 * q^39 - 93 * q^40 - 3 * q^41 + 75 * q^42 - 4 * q^43 - 107 * q^44 - 39 * q^45 - 95 * q^46 + 60 * q^47 + 25 * q^48 - 108 * q^49 + 47 * q^51 + 13 * q^52 + 10 * q^53 + 55 * q^54 + 32 * q^55 - 10 * q^56 - 74 * q^57 + 42 * q^58 + 41 * q^59 + 200 * q^60 - 350 * q^62 - 42 * q^63 + 200 * q^64 + 89 * q^65 - 16 * q^66 - 31 * q^67 + 26 * q^68 + 30 * q^69 - 44 * q^70 - 23 * q^71 - 19 * q^73 + 48 * q^74 - 9 * q^75 + 37 * q^76 - 3 * q^77 - 85 * q^78 - 61 * q^79 - 73 * q^80 - 94 * q^81 + 66 * q^82 + 7 * q^83 - 190 * q^84 + 10 * q^85 - 52 * q^86 + 61 * q^87 + 22 * q^88 + 15 * q^89 - 153 * q^90 - 72 * q^91 - 59 * q^92 + 3 * q^93 - 10 * q^94 - 3 * q^95 - 100 * q^96 + 36 * q^97 + 25 * q^98 - 125 * 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

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