Space of modular forms of level 3971, weight 2, and Character 3971.p

• Label: 3971.2.p
• Level: $3971$
• Weight: $2$
• Character orbit: 3971.p
• Rep. character: $\chi_{3971}(307,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $1944$
• Sturm bound: $760$

Defining parameters

Level:	$N$	$=$	$3971 = 11 \cdot 19^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3971.p (of order $18$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$209$
Character field:			$\Q(\zeta_{18})$
Sturm bound:			$760$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3971, [\chi])$.

	Total	New	Old
Modular forms	2400	2136	264
Cusp forms	2160	1944	216
Eisenstein series	240	192	48

Trace form

1944 * q + 6 * q^3 + 12 * q^4 + 12 * q^5 - 6 * q^9 + 9 * q^11 + 18 * q^12 + 36 * q^15 - 348 * q^20 + 36 * q^22 + 12 * q^23 + 12 * q^25 + 114 * q^26 + 36 * q^27 - 45 * q^33 - 60 * q^34 + 72 * q^36 + 66 * q^42 - 3 * q^44 - 90 * q^45 + 84 * q^47 - 102 * q^48 + 642 * q^49 + 66 * q^53 - 48 * q^55 - 168 * q^58 - 6 * q^59 + 138 * q^60 - 630 * q^64 - 117 * q^66 + 102 * q^67 + 72 * q^69 - 174 * q^70 - 30 * q^71 - 144 * q^77 + 84 * q^78 - 216 * q^81 - 48 * q^82 + 36 * q^86 + 27 * q^88 + 84 * q^89 + 6 * q^91 - 30 * q^92 - 54 * q^93 - 42 * q^97 - 63 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(3971, [\chi])$ into newform subspaces

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

Decomposition of $S_{2}^{\mathrm{old}}(3971, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3971, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(209, [\chi])$$^{\oplus 2}$