Space of modular forms of level 3700, weight 2, and Character 3700.el

• Label: 3700.2.el
• Level: $3700$
• Weight: $2$
• Character orbit: 3700.el
• Rep. character: $\chi_{3700}(19,\cdot)$
• Character field: $\Q(\zeta_{180})$
• Dimension: $27168$
• Sturm bound: $1140$

Defining parameters

Level:	\( N \)	\(=\)	\( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3700.el (of order \(180\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3700 \)
Character field:			\(\Q(\zeta_{180})\)
Sturm bound:			\(1140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3700, [\chi])\).

	Total	New	Old
Modular forms	27552	27552	0
Cusp forms	27168	27168	0
Eisenstein series	384	384	0

Trace form

27168 * q - 60 * q^2 - 36 * q^4 - 102 * q^5 - 36 * q^6 - 60 * q^8 - 72 * q^9 - 24 * q^10 - 60 * q^12 - 120 * q^13 - 36 * q^14 - 36 * q^16 - 120 * q^17 - 48 * q^20 - 72 * q^21 - 60 * q^22 - 180 * q^24 - 126 * q^25 - 48 * q^26 - 60 * q^28 - 72 * q^29 - 108 * q^30 - 120 * q^33 - 36 * q^34 - 120 * q^37 - 120 * q^38 - 48 * q^40 - 72 * q^41 - 60 * q^42 - 84 * q^44 - 96 * q^45 - 156 * q^46 - 90 * q^48 - 192 * q^49 - 48 * q^50 - 360 * q^52 - 120 * q^53 - 12 * q^54 - 36 * q^56 + 300 * q^58 - 312 * q^60 - 72 * q^61 - 60 * q^62 - 54 * q^64 + 216 * q^65 - 108 * q^66 - 72 * q^69 + 252 * q^70 - 60 * q^72 - 96 * q^74 - 96 * q^76 - 540 * q^77 - 150 * q^78 + 84 * q^80 - 162 * q^84 - 144 * q^85 - 36 * q^86 - 60 * q^88 - 72 * q^89 + 96 * q^90 - 60 * q^92 - 60 * q^94 - 36 * q^96 - 120 * q^97 - 60 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(3700, [\chi])\) into newform subspaces

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