Space of modular forms of level 1815 and weight 2

• Label: 1815.2
• Level: 1815
• Weight: 2
• Dimension: 77700
• Nonzero newspaces: 24
• Sturm bound: 464640
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(464640\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1815))\).

	Total	New	Old
Modular forms	118720	79388	39332
Cusp forms	113601	77700	35901
Eisenstein series	5119	1688	3431

Trace form

77700 * q - 4 * q^2 - 92 * q^3 - 188 * q^4 - 252 * q^6 - 148 * q^7 + 68 * q^8 - 50 * q^9 - 214 * q^10 + 20 * q^11 - 96 * q^12 - 156 * q^13 + 96 * q^14 - 97 * q^15 - 332 * q^16 + 104 * q^17 - 34 * q^18 - 76 * q^19 + 92 * q^20 - 178 * q^21 - 80 * q^22 + 56 * q^23 - 8 * q^24 - 190 * q^25 + 160 * q^26 - 152 * q^27 - 36 * q^28 + 48 * q^29 - 127 * q^30 - 492 * q^31 + 12 * q^32 - 120 * q^33 - 236 * q^34 + 72 * q^35 - 258 * q^36 - 68 * q^37 + 136 * q^38 - 2 * q^39 - 382 * q^40 + 208 * q^41 - 54 * q^42 - 100 * q^43 + 60 * q^44 - 165 * q^45 - 412 * q^46 - 140 * q^48 - 204 * q^49 - 104 * q^50 - 230 * q^51 - 396 * q^52 - 24 * q^53 - 152 * q^54 - 380 * q^55 - 280 * q^56 - 294 * q^57 - 548 * q^58 - 184 * q^59 - 411 * q^60 - 724 * q^61 - 176 * q^62 - 238 * q^63 - 540 * q^64 - 136 * q^65 - 390 * q^66 - 436 * q^67 - 48 * q^68 - 154 * q^69 - 154 * q^70 + 160 * q^71 - 122 * q^72 + 116 * q^73 + 256 * q^74 + 3 * q^75 + 76 * q^76 + 180 * q^77 - 14 * q^78 + 260 * q^79 + 388 * q^80 - 230 * q^81 + 124 * q^82 + 448 * q^83 - 46 * q^84 - 26 * q^85 + 424 * q^86 + 142 * q^87 + 120 * q^88 + 224 * q^89 - 369 * q^90 - 372 * q^91 + 112 * q^92 - 42 * q^93 - 292 * q^94 - 36 * q^95 - 628 * q^96 - 276 * q^97 - 164 * q^98 - 240 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)

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
1815.2.a	\(\chi_{1815}(1, \cdot)\)	1815.2.a.a	1	1
		1815.2.a.b	1
		1815.2.a.c	1
		1815.2.a.d	1
		1815.2.a.e	1
		1815.2.a.f	2
		1815.2.a.g	2
		1815.2.a.h	2
		1815.2.a.i	2
		1815.2.a.j	2
		1815.2.a.k	2
		1815.2.a.l	3
		1815.2.a.m	3
		1815.2.a.n	3
		1815.2.a.o	4
		1815.2.a.p	4
		1815.2.a.q	4
		1815.2.a.r	4
		1815.2.a.s	4
		1815.2.a.t	4
		1815.2.a.u	4
		1815.2.a.v	4
		1815.2.a.w	4
		1815.2.a.x	4
		1815.2.a.y	6
1815.2.c	\(\chi_{1815}(364, \cdot)\)	1815.2.c.a	2	1
		1815.2.c.b	2
		1815.2.c.c	4
		1815.2.c.d	6
		1815.2.c.e	6
		1815.2.c.f	8
		1815.2.c.g	8
		1815.2.c.h	12
		1815.2.c.i	12
		1815.2.c.j	24
		1815.2.c.k	24
1815.2.d	\(\chi_{1815}(1814, \cdot)\)	n/a	200	1
1815.2.f	\(\chi_{1815}(1451, \cdot)\)	n/a	144	1
1815.2.j	\(\chi_{1815}(967, \cdot)\)	n/a	216	2
1815.2.k	\(\chi_{1815}(122, \cdot)\)	n/a	400	2
1815.2.m	\(\chi_{1815}(511, \cdot)\)	n/a	288	4
1815.2.p	\(\chi_{1815}(161, \cdot)\)	n/a	576	4
1815.2.r	\(\chi_{1815}(239, \cdot)\)	n/a	800	4
1815.2.s	\(\chi_{1815}(124, \cdot)\)	n/a	432	4
1815.2.u	\(\chi_{1815}(166, \cdot)\)	n/a	880	10
1815.2.w	\(\chi_{1815}(323, \cdot)\)	n/a	1600	8
1815.2.x	\(\chi_{1815}(112, \cdot)\)	n/a	864	8
1815.2.bb	\(\chi_{1815}(131, \cdot)\)	n/a	1760	10
1815.2.bd	\(\chi_{1815}(164, \cdot)\)	n/a	2600	10
1815.2.be	\(\chi_{1815}(34, \cdot)\)	n/a	1320	10
1815.2.bh	\(\chi_{1815}(23, \cdot)\)	n/a	5200	20
1815.2.bi	\(\chi_{1815}(43, \cdot)\)	n/a	2640	20
1815.2.bk	\(\chi_{1815}(16, \cdot)\)	n/a	3520	40
1815.2.bm	\(\chi_{1815}(4, \cdot)\)	n/a	5280	40
1815.2.bn	\(\chi_{1815}(29, \cdot)\)	n/a	10400	40
1815.2.bp	\(\chi_{1815}(41, \cdot)\)	n/a	7040	40
1815.2.bt	\(\chi_{1815}(7, \cdot)\)	n/a	10560	80
1815.2.bu	\(\chi_{1815}(38, \cdot)\)	n/a	20800	80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1815))\) into lower level spaces

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