Space of modular forms of level 3751 and weight 2

• Label: 3751.2
• Level: 3751
• Weight: 2
• Dimension: 565977
• Nonzero newspaces: 56
• Sturm bound: 2323200
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 3751 = 11^{2} \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(2323200\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3751))\).

	Total	New	Old
Modular forms	585600	574125	11475
Cusp forms	576001	565977	10024
Eisenstein series	9599	8148	1451

Trace form

565977 * q - 1269 * q^2 - 1267 * q^3 - 1261 * q^4 - 1263 * q^5 - 1271 * q^6 - 1279 * q^7 - 1285 * q^8 - 1289 * q^9 - 1299 * q^10 - 1410 * q^11 - 2419 * q^12 - 1267 * q^13 - 1287 * q^14 - 1307 * q^15 - 1333 * q^16 - 1299 * q^17 - 1317 * q^18 - 1295 * q^19 - 1331 * q^20 - 1316 * q^21 - 1460 * q^22 - 2422 * q^23 - 1435 * q^24 - 1368 * q^25 - 1401 * q^26 - 1360 * q^27 - 1463 * q^28 - 1345 * q^29 - 1466 * q^30 - 1358 * q^31 - 2804 * q^32 - 1480 * q^33 - 2507 * q^34 - 1389 * q^35 - 1533 * q^36 - 1364 * q^37 - 1405 * q^38 - 1418 * q^39 - 1495 * q^40 - 1386 * q^41 - 1493 * q^42 - 1372 * q^43 - 1540 * q^44 - 2519 * q^45 - 1391 * q^46 - 1319 * q^47 - 1532 * q^48 - 1411 * q^49 - 1484 * q^50 - 1481 * q^51 - 1494 * q^52 - 1417 * q^53 - 1700 * q^54 - 1520 * q^55 - 2730 * q^56 - 1505 * q^57 - 1540 * q^58 - 1385 * q^59 - 1854 * q^60 - 1436 * q^61 - 1524 * q^62 - 2932 * q^63 - 1661 * q^64 - 1497 * q^65 - 1650 * q^66 - 2549 * q^67 - 1628 * q^68 - 1533 * q^69 - 1662 * q^70 - 1471 * q^71 - 1810 * q^72 - 1417 * q^73 - 1582 * q^74 - 1592 * q^75 - 1660 * q^76 - 1570 * q^77 - 2794 * q^78 - 1490 * q^79 - 1793 * q^80 - 1553 * q^81 - 1503 * q^82 - 1552 * q^83 - 1867 * q^84 - 1539 * q^85 - 1591 * q^86 - 1555 * q^87 - 1720 * q^88 - 2550 * q^89 - 1932 * q^90 - 1576 * q^91 - 1794 * q^92 - 1572 * q^93 - 3032 * q^94 - 1615 * q^95 - 2016 * q^96 - 1544 * q^97 - 1753 * q^98 - 1680 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3751))\)

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
3751.2.a	\(\chi_{3751}(1, \cdot)\)	3751.2.a.a	2	1
		3751.2.a.b	2
		3751.2.a.c	3
		3751.2.a.d	3
		3751.2.a.e	4
		3751.2.a.f	4
		3751.2.a.g	4
		3751.2.a.h	8
		3751.2.a.i	9
		3751.2.a.j	9
		3751.2.a.k	11
		3751.2.a.l	15
		3751.2.a.m	15
		3751.2.a.n	16
		3751.2.a.o	16
		3751.2.a.p	30
		3751.2.a.q	30
		3751.2.a.r	30
		3751.2.a.s	30
		3751.2.a.t	32
3751.2.b	\(\chi_{3751}(3750, \cdot)\)	n/a	280	1
3751.2.e	\(\chi_{3751}(1090, \cdot)\)	n/a	564	2
3751.2.f	\(\chi_{3751}(686, \cdot)\)	n/a	1120	4
3751.2.g	\(\chi_{3751}(729, \cdot)\)	n/a	1120	4
3751.2.h	\(\chi_{3751}(807, \cdot)\)	n/a	1080	4
3751.2.i	\(\chi_{3751}(969, \cdot)\)	n/a	1124	4
3751.2.j	\(\chi_{3751}(977, \cdot)\)	n/a	1120	4
3751.2.k	\(\chi_{3751}(202, \cdot)\)	n/a	1120	4
3751.2.m	\(\chi_{3751}(967, \cdot)\)	n/a	560	2
3751.2.p	\(\chi_{3751}(457, \cdot)\)	n/a	1120	4
3751.2.v	\(\chi_{3751}(215, \cdot)\)	n/a	1120	4
3751.2.ba	\(\chi_{3751}(1425, \cdot)\)	n/a	1120	4
3751.2.bb	\(\chi_{3751}(959, \cdot)\)	n/a	1120	4
3751.2.bc	\(\chi_{3751}(1201, \cdot)\)	n/a	1120	4
3751.2.bd	\(\chi_{3751}(120, \cdot)\)	n/a	1120	4
3751.2.bg	\(\chi_{3751}(342, \cdot)\)	n/a	3300	10
3751.2.bh	\(\chi_{3751}(493, \cdot)\)	n/a	2240	8
3751.2.bi	\(\chi_{3751}(485, \cdot)\)	n/a	2256	8
3751.2.bj	\(\chi_{3751}(366, \cdot)\)	n/a	2240	8
3751.2.bk	\(\chi_{3751}(9, \cdot)\)	n/a	2240	8
3751.2.bl	\(\chi_{3751}(390, \cdot)\)	n/a	2240	8
3751.2.bm	\(\chi_{3751}(608, \cdot)\)	n/a	2240	8
3751.2.bo	\(\chi_{3751}(340, \cdot)\)	n/a	3500	10
3751.2.bq	\(\chi_{3751}(282, \cdot)\)	n/a	2240	8
3751.2.by	\(\chi_{3751}(241, \cdot)\)	n/a	2240	8
3751.2.bz	\(\chi_{3751}(602, \cdot)\)	n/a	2240	8
3751.2.ca	\(\chi_{3751}(239, \cdot)\)	n/a	2240	8
3751.2.cb	\(\chi_{3751}(161, \cdot)\)	n/a	2240	8
3751.2.cg	\(\chi_{3751}(354, \cdot)\)	n/a	2240	8
3751.2.ci	\(\chi_{3751}(56, \cdot)\)	n/a	7000	20
3751.2.cj	\(\chi_{3751}(97, \cdot)\)	n/a	14000	40
3751.2.ck	\(\chi_{3751}(78, \cdot)\)	n/a	14000	40
3751.2.cl	\(\chi_{3751}(125, \cdot)\)	n/a	13200	40
3751.2.cm	\(\chi_{3751}(47, \cdot)\)	n/a	14000	40
3751.2.cn	\(\chi_{3751}(4, \cdot)\)	n/a	14000	40
3751.2.co	\(\chi_{3751}(70, \cdot)\)	n/a	14000	40
3751.2.cr	\(\chi_{3751}(274, \cdot)\)	n/a	7000	20
3751.2.ct	\(\chi_{3751}(46, \cdot)\)	n/a	14000	40
3751.2.cy	\(\chi_{3751}(54, \cdot)\)	n/a	14000	40
3751.2.cz	\(\chi_{3751}(29, \cdot)\)	n/a	14000	40
3751.2.da	\(\chi_{3751}(85, \cdot)\)	n/a	14000	40
3751.2.db	\(\chi_{3751}(30, \cdot)\)	n/a	14000	40
3751.2.dj	\(\chi_{3751}(116, \cdot)\)	n/a	14000	40
3751.2.dk	\(\chi_{3751}(20, \cdot)\)	n/a	28000	80
3751.2.dl	\(\chi_{3751}(69, \cdot)\)	n/a	28000	80
3751.2.dm	\(\chi_{3751}(14, \cdot)\)	n/a	28000	80
3751.2.dn	\(\chi_{3751}(38, \cdot)\)	n/a	28000	80
3751.2.do	\(\chi_{3751}(5, \cdot)\)	n/a	28000	80
3751.2.dp	\(\chi_{3751}(45, \cdot)\)	n/a	28000	80
3751.2.ds	\(\chi_{3751}(6, \cdot)\)	n/a	28000	80
3751.2.dt	\(\chi_{3751}(73, \cdot)\)	n/a	28000	80
3751.2.du	\(\chi_{3751}(79, \cdot)\)	n/a	28000	80
3751.2.dv	\(\chi_{3751}(21, \cdot)\)	n/a	28000	80
3751.2.ea	\(\chi_{3751}(13, \cdot)\)	n/a	28000	80
3751.2.eg	\(\chi_{3751}(17, \cdot)\)	n/a	28000	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3751))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3751)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(341))\)\(^{\oplus 2}\)