Space of modular forms of level 1815 and weight 4

• Label: 1815.4
• Level: 1815
• Weight: 4
• Dimension: 234794
• Nonzero newspaces: 24
• Sturm bound: 929280
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(929280\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1815))\).

	Total	New	Old
Modular forms	351040	236482	114558
Cusp forms	345920	234794	111126
Eisenstein series	5120	1688	3432

Trace form

234794 * q + 4 * q^2 - 96 * q^3 - 204 * q^4 + 6 * q^5 - 70 * q^6 - 120 * q^7 - 356 * q^8 - 428 * q^9 - 746 * q^10 - 200 * q^11 - 702 * q^12 - 176 * q^13 + 1824 * q^14 + 659 * q^15 + 2804 * q^16 + 1240 * q^17 + 266 * q^18 - 2236 * q^19 - 2336 * q^20 - 2518 * q^21 - 2720 * q^22 - 1808 * q^23 - 4418 * q^24 - 904 * q^25 + 32 * q^26 + 732 * q^27 + 4716 * q^28 + 3588 * q^29 + 4851 * q^30 + 5612 * q^31 + 7236 * q^32 + 3510 * q^33 + 6612 * q^34 + 1800 * q^35 + 3914 * q^36 - 1600 * q^37 - 2992 * q^38 - 4994 * q^39 - 8602 * q^40 - 9244 * q^41 - 17702 * q^42 - 12808 * q^43 - 10500 * q^44 - 5469 * q^45 - 13068 * q^46 - 4968 * q^47 - 5290 * q^48 + 1650 * q^49 + 7424 * q^50 + 1826 * q^51 + 21124 * q^52 + 13872 * q^53 + 1834 * q^54 + 9740 * q^55 + 34720 * q^56 + 11966 * q^57 + 19996 * q^58 + 4576 * q^59 + 14511 * q^60 + 9056 * q^61 + 10712 * q^62 + 16382 * q^63 + 2004 * q^64 - 6032 * q^65 + 7750 * q^66 - 11336 * q^67 - 21288 * q^68 + 834 * q^69 - 21370 * q^70 + 6752 * q^71 - 2634 * q^72 + 18680 * q^73 + 4424 * q^74 - 4521 * q^75 - 20420 * q^76 - 1800 * q^77 - 30450 * q^78 - 16100 * q^79 - 18616 * q^80 - 30776 * q^81 - 47308 * q^82 - 29512 * q^83 - 46454 * q^84 - 20978 * q^85 - 19456 * q^86 - 21706 * q^87 - 22760 * q^88 - 14876 * q^89 - 13701 * q^90 - 27428 * q^91 - 33544 * q^92 - 12826 * q^93 - 17924 * q^94 - 21816 * q^95 + 18358 * q^96 + 3624 * q^97 + 404 * q^98 + 9440 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1815))\)

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
1815.4.a	\(\chi_{1815}(1, \cdot)\)	1815.4.a.a	1	1
		1815.4.a.b	1
		1815.4.a.c	1
		1815.4.a.d	1
		1815.4.a.e	1
		1815.4.a.f	1
		1815.4.a.g	1
		1815.4.a.h	1
		1815.4.a.i	2
		1815.4.a.j	2
		1815.4.a.k	2
		1815.4.a.l	2
		1815.4.a.m	2
		1815.4.a.n	2
		1815.4.a.o	2
		1815.4.a.p	3
		1815.4.a.q	3
		1815.4.a.r	3
		1815.4.a.s	3
		1815.4.a.t	4
		1815.4.a.u	4
		1815.4.a.v	4
		1815.4.a.w	4
		1815.4.a.x	5
		1815.4.a.y	5
		1815.4.a.z	6
		1815.4.a.ba	6
		1815.4.a.bb	6
		1815.4.a.bc	7
		1815.4.a.bd	7
		1815.4.a.be	8
		1815.4.a.bf	10
		1815.4.a.bg	12
		1815.4.a.bh	12
		1815.4.a.bi	12
		1815.4.a.bj	12
		1815.4.a.bk	12
		1815.4.a.bl	12
		1815.4.a.bm	12
		1815.4.a.bn	12
		1815.4.a.bo	12
1815.4.c	\(\chi_{1815}(364, \cdot)\)	n/a	328	1
1815.4.d	\(\chi_{1815}(1814, \cdot)\)	n/a	632	1
1815.4.f	\(\chi_{1815}(1451, \cdot)\)	n/a	432	1
1815.4.j	\(\chi_{1815}(967, \cdot)\)	n/a	648	2
1815.4.k	\(\chi_{1815}(122, \cdot)\)	n/a	1272	2
1815.4.m	\(\chi_{1815}(511, \cdot)\)	n/a	864	4
1815.4.p	\(\chi_{1815}(161, \cdot)\)	n/a	1728	4
1815.4.r	\(\chi_{1815}(239, \cdot)\)	n/a	2528	4
1815.4.s	\(\chi_{1815}(124, \cdot)\)	n/a	1296	4
1815.4.u	\(\chi_{1815}(166, \cdot)\)	n/a	2640	10
1815.4.w	\(\chi_{1815}(323, \cdot)\)	n/a	5056	8
1815.4.x	\(\chi_{1815}(112, \cdot)\)	n/a	2592	8
1815.4.bb	\(\chi_{1815}(131, \cdot)\)	n/a	5280	10
1815.4.bd	\(\chi_{1815}(164, \cdot)\)	n/a	7880	10
1815.4.be	\(\chi_{1815}(34, \cdot)\)	n/a	3960	10
1815.4.bh	\(\chi_{1815}(23, \cdot)\)	n/a	15760	20
1815.4.bi	\(\chi_{1815}(43, \cdot)\)	n/a	7920	20
1815.4.bk	\(\chi_{1815}(16, \cdot)\)	n/a	10560	40
1815.4.bm	\(\chi_{1815}(4, \cdot)\)	n/a	15840	40
1815.4.bn	\(\chi_{1815}(29, \cdot)\)	n/a	31520	40
1815.4.bp	\(\chi_{1815}(41, \cdot)\)	n/a	21120	40
1815.4.bt	\(\chi_{1815}(7, \cdot)\)	n/a	31680	80
1815.4.bu	\(\chi_{1815}(38, \cdot)\)	n/a	63040	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1815))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1815)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)