Space of modular forms of level 3971 and weight 2

• Label: 3971.2
• Level: 3971
• Weight: 2
• Dimension: 631220
• Nonzero newspaces: 24
• Sturm bound: 2599200
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(2599200\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3971))\).

	Total	New	Old
Modular forms	654840	639652	15188
Cusp forms	644761	631220	13541
Eisenstein series	10079	8432	1647

Trace form

631220 * q - 1223 * q^2 - 1221 * q^3 - 1215 * q^4 - 1217 * q^5 - 1210 * q^6 - 1218 * q^7 - 1209 * q^8 - 1213 * q^9 - 1208 * q^10 - 1375 * q^11 - 2776 * q^12 - 1254 * q^13 - 1268 * q^14 - 1273 * q^15 - 1341 * q^16 - 1244 * q^17 - 1325 * q^18 - 1338 * q^19 - 2476 * q^20 - 1274 * q^21 - 1430 * q^22 - 2767 * q^23 - 1308 * q^24 - 1269 * q^25 - 1262 * q^26 - 1263 * q^27 - 1328 * q^28 - 1266 * q^29 - 1402 * q^30 - 1257 * q^31 - 1333 * q^32 - 1482 * q^33 - 2876 * q^34 - 1322 * q^35 - 1569 * q^36 - 1291 * q^37 - 1422 * q^38 - 2540 * q^39 - 1458 * q^40 - 1262 * q^41 - 1492 * q^42 - 1342 * q^43 - 1512 * q^44 - 3002 * q^45 - 1474 * q^46 - 1348 * q^47 - 1600 * q^48 - 1326 * q^49 - 1519 * q^50 - 1366 * q^51 - 1382 * q^52 - 1320 * q^53 - 1438 * q^54 - 1442 * q^55 - 3102 * q^56 - 1386 * q^57 - 2430 * q^58 - 1339 * q^59 - 1670 * q^60 - 1414 * q^61 - 1538 * q^62 - 1452 * q^63 - 1657 * q^64 - 1532 * q^65 - 1651 * q^66 - 3065 * q^67 - 1606 * q^68 - 1523 * q^69 - 1652 * q^70 - 1407 * q^71 - 1821 * q^72 - 1482 * q^73 - 1476 * q^74 - 1468 * q^75 - 1476 * q^76 - 2865 * q^77 - 3154 * q^78 - 1562 * q^79 - 1690 * q^80 - 1570 * q^81 - 1766 * q^82 - 1398 * q^83 - 1860 * q^84 - 1550 * q^85 - 1476 * q^86 - 1680 * q^87 - 1686 * q^88 - 2973 * q^89 - 1814 * q^90 - 1456 * q^91 - 1526 * q^92 - 1511 * q^93 - 1564 * q^94 - 1422 * q^95 - 2996 * q^96 - 1385 * q^97 - 1731 * q^98 - 1636 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3971))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
3971.2.a	\(\chi_{3971}(1, \cdot)\)	3971.2.a.a	1	1
		3971.2.a.b	1
		3971.2.a.c	2
		3971.2.a.d	2
		3971.2.a.e	3
		3971.2.a.f	3
		3971.2.a.g	4
		3971.2.a.h	5
		3971.2.a.i	7
		3971.2.a.j	9
		3971.2.a.k	9
		3971.2.a.l	9
		3971.2.a.m	9
		3971.2.a.n	10
		3971.2.a.o	10
		3971.2.a.p	10
		3971.2.a.q	18
		3971.2.a.r	18
		3971.2.a.s	21
		3971.2.a.t	21
		3971.2.a.u	24
		3971.2.a.v	24
		3971.2.a.w	24
		3971.2.a.x	40
3971.2.d	\(\chi_{3971}(3970, \cdot)\)	n/a	324	1
3971.2.e	\(\chi_{3971}(2234, \cdot)\)	n/a	564	2
3971.2.f	\(\chi_{3971}(1445, \cdot)\)	n/a	1296	4
3971.2.g	\(\chi_{3971}(791, \cdot)\)	n/a	648	2
3971.2.j	\(\chi_{3971}(595, \cdot)\)	n/a	1704	6
3971.2.k	\(\chi_{3971}(360, \cdot)\)	n/a	1296	4
3971.2.n	\(\chi_{3971}(653, \cdot)\)	n/a	2592	8
3971.2.p	\(\chi_{3971}(307, \cdot)\)	n/a	1944	6
3971.2.r	\(\chi_{3971}(210, \cdot)\)	n/a	5724	18
3971.2.u	\(\chi_{3971}(293, \cdot)\)	n/a	2592	8
3971.2.v	\(\chi_{3971}(208, \cdot)\)	n/a	6804	18
3971.2.y	\(\chi_{3971}(234, \cdot)\)	n/a	7776	24
3971.2.z	\(\chi_{3971}(45, \cdot)\)	n/a	11448	36
3971.2.bb	\(\chi_{3971}(116, \cdot)\)	n/a	7776	24
3971.2.bd	\(\chi_{3971}(20, \cdot)\)	n/a	27216	72
3971.2.bg	\(\chi_{3971}(65, \cdot)\)	n/a	13608	36
3971.2.bh	\(\chi_{3971}(23, \cdot)\)	n/a	34128	108
3971.2.bk	\(\chi_{3971}(18, \cdot)\)	n/a	27216	72
3971.2.bl	\(\chi_{3971}(26, \cdot)\)	n/a	54432	144
3971.2.bn	\(\chi_{3971}(10, \cdot)\)	n/a	40824	108
3971.2.bp	\(\chi_{3971}(8, \cdot)\)	n/a	54432	144
3971.2.bs	\(\chi_{3971}(4, \cdot)\)	n/a	163296	432
3971.2.bu	\(\chi_{3971}(2, \cdot)\)	n/a	163296	432

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3971))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3971)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(209))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3971))\)\(^{\oplus 1}\)