Space of modular forms of level 3675 and weight 2

• Label: 3675.2
• Level: 3675
• Weight: 2
• Dimension: 310043
• Nonzero newspaces: 48
• Sturm bound: 1881600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(1881600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3675))\).

	Total	New	Old
Modular forms	477120	314019	163101
Cusp forms	463681	310043	153638
Eisenstein series	13439	3976	9463

Trace form

310043 * q - q^2 - 206 * q^3 - 431 * q^4 - 6 * q^5 - 356 * q^6 - 476 * q^7 - 57 * q^8 - 222 * q^9 - 514 * q^10 - 40 * q^11 - 240 * q^12 - 460 * q^13 - 24 * q^14 - 446 * q^15 - 735 * q^16 - 26 * q^17 - 202 * q^18 - 438 * q^19 + 36 * q^20 - 385 * q^21 - 758 * q^22 - 32 * q^23 + 6 * q^24 - 418 * q^25 + 102 * q^26 - 74 * q^27 - 348 * q^28 + 134 * q^29 - 82 * q^30 - 554 * q^31 + 461 * q^32 - 7 * q^33 - 62 * q^34 + 72 * q^35 - 182 * q^36 - 166 * q^37 + 368 * q^38 + 72 * q^39 - 190 * q^40 + 206 * q^41 - 21 * q^42 - 522 * q^43 + 516 * q^44 - 104 * q^45 - 330 * q^46 + 88 * q^47 + 285 * q^48 - 354 * q^49 + 106 * q^50 - 543 * q^51 + 204 * q^52 + 44 * q^53 - 86 * q^54 - 380 * q^55 + 342 * q^56 - 159 * q^57 + 392 * q^58 + 328 * q^59 + 14 * q^60 - 146 * q^61 + 688 * q^62 - 204 * q^63 + 201 * q^64 + 230 * q^65 + 125 * q^66 + 122 * q^67 + 670 * q^68 + 79 * q^69 - 216 * q^70 + 208 * q^71 - 24 * q^72 + 164 * q^73 + 718 * q^74 - 162 * q^75 - 494 * q^76 + 216 * q^77 + 107 * q^78 + 110 * q^79 + 278 * q^80 - 282 * q^81 + 434 * q^82 + 356 * q^83 - 4 * q^84 - 634 * q^85 + 422 * q^86 - 143 * q^87 + 508 * q^88 + 120 * q^89 - 456 * q^90 - 698 * q^91 - 10 * q^92 - 233 * q^93 - 164 * q^94 + 56 * q^95 - 777 * q^96 - 242 * q^97 + 438 * q^98 - 880 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3675))\)

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
3675.2.a	\(\chi_{3675}(1, \cdot)\)	3675.2.a.a	1	1
		3675.2.a.b	1
		3675.2.a.c	1
		3675.2.a.d	1
		3675.2.a.e	1
		3675.2.a.f	1
		3675.2.a.g	1
		3675.2.a.h	1
		3675.2.a.i	1
		3675.2.a.j	1
		3675.2.a.k	1
		3675.2.a.l	1
		3675.2.a.m	1
		3675.2.a.n	1
		3675.2.a.o	1
		3675.2.a.p	1
		3675.2.a.q	1
		3675.2.a.r	2
		3675.2.a.s	2
		3675.2.a.t	2
		3675.2.a.u	2
		3675.2.a.v	2
		3675.2.a.w	2
		3675.2.a.x	2
		3675.2.a.y	2
		3675.2.a.z	2
		3675.2.a.ba	2
		3675.2.a.bb	2
		3675.2.a.bc	2
		3675.2.a.bd	2
		3675.2.a.be	2
		3675.2.a.bf	2
		3675.2.a.bg	2
		3675.2.a.bh	2
		3675.2.a.bi	3
		3675.2.a.bj	3
		3675.2.a.bk	4
		3675.2.a.bl	4
		3675.2.a.bm	4
		3675.2.a.bn	4
		3675.2.a.bo	4
		3675.2.a.bp	4
		3675.2.a.bq	4
		3675.2.a.br	4
		3675.2.a.bs	4
		3675.2.a.bt	4
		3675.2.a.bu	4
		3675.2.a.bv	4
		3675.2.a.bw	4
		3675.2.a.bx	4
		3675.2.a.by	4
		3675.2.a.bz	4
		3675.2.a.ca	4
		3675.2.a.cb	4
3675.2.b	\(\chi_{3675}(2351, \cdot)\)	n/a	242	1
3675.2.d	\(\chi_{3675}(1324, \cdot)\)	n/a	124	1
3675.2.g	\(\chi_{3675}(3674, \cdot)\)	n/a	232	1
3675.2.i	\(\chi_{3675}(226, \cdot)\)	n/a	254	2
3675.2.j	\(\chi_{3675}(932, \cdot)\)	n/a	472	2
3675.2.m	\(\chi_{3675}(832, \cdot)\)	n/a	240	2
3675.2.n	\(\chi_{3675}(736, \cdot)\)	n/a	824	4
3675.2.q	\(\chi_{3675}(374, \cdot)\)	n/a	464	2
3675.2.r	\(\chi_{3675}(949, \cdot)\)	n/a	240	2
3675.2.t	\(\chi_{3675}(2126, \cdot)\)	n/a	482	2
3675.2.v	\(\chi_{3675}(526, \cdot)\)	n/a	1068	6
3675.2.x	\(\chi_{3675}(734, \cdot)\)	n/a	1568	4
3675.2.ba	\(\chi_{3675}(589, \cdot)\)	n/a	816	4
3675.2.bc	\(\chi_{3675}(146, \cdot)\)	n/a	1568	4
3675.2.bd	\(\chi_{3675}(607, \cdot)\)	n/a	480	4
3675.2.bg	\(\chi_{3675}(557, \cdot)\)	n/a	928	4
3675.2.bi	\(\chi_{3675}(524, \cdot)\)	n/a	1992	6
3675.2.bl	\(\chi_{3675}(274, \cdot)\)	n/a	1008	6
3675.2.bn	\(\chi_{3675}(251, \cdot)\)	n/a	2088	6
3675.2.bo	\(\chi_{3675}(361, \cdot)\)	n/a	1600	8
3675.2.bp	\(\chi_{3675}(97, \cdot)\)	n/a	1600	8
3675.2.bs	\(\chi_{3675}(197, \cdot)\)	n/a	3200	8
3675.2.bt	\(\chi_{3675}(151, \cdot)\)	n/a	2124	12
3675.2.bv	\(\chi_{3675}(118, \cdot)\)	n/a	2016	12
3675.2.bw	\(\chi_{3675}(218, \cdot)\)	n/a	3984	12
3675.2.bz	\(\chi_{3675}(521, \cdot)\)	n/a	3136	8
3675.2.cb	\(\chi_{3675}(79, \cdot)\)	n/a	1600	8
3675.2.cc	\(\chi_{3675}(509, \cdot)\)	n/a	3136	8
3675.2.cf	\(\chi_{3675}(106, \cdot)\)	n/a	6720	24
3675.2.ch	\(\chi_{3675}(26, \cdot)\)	n/a	4188	12
3675.2.cj	\(\chi_{3675}(424, \cdot)\)	n/a	2016	12
3675.2.ck	\(\chi_{3675}(299, \cdot)\)	n/a	3984	12
3675.2.cn	\(\chi_{3675}(128, \cdot)\)	n/a	6272	16
3675.2.cq	\(\chi_{3675}(178, \cdot)\)	n/a	3200	16
3675.2.cr	\(\chi_{3675}(41, \cdot)\)	n/a	13344	24
3675.2.ct	\(\chi_{3675}(64, \cdot)\)	n/a	6720	24
3675.2.cw	\(\chi_{3675}(104, \cdot)\)	n/a	13344	24
3675.2.cz	\(\chi_{3675}(32, \cdot)\)	n/a	7968	24
3675.2.da	\(\chi_{3675}(82, \cdot)\)	n/a	4032	24
3675.2.dc	\(\chi_{3675}(16, \cdot)\)	n/a	13440	48
3675.2.de	\(\chi_{3675}(8, \cdot)\)	n/a	26688	48
3675.2.df	\(\chi_{3675}(13, \cdot)\)	n/a	13440	48
3675.2.dj	\(\chi_{3675}(59, \cdot)\)	n/a	26688	48
3675.2.dk	\(\chi_{3675}(4, \cdot)\)	n/a	13440	48
3675.2.dm	\(\chi_{3675}(131, \cdot)\)	n/a	26688	48
3675.2.dp	\(\chi_{3675}(52, \cdot)\)	n/a	26880	96
3675.2.dq	\(\chi_{3675}(2, \cdot)\)	n/a	53376	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3675))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3675)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 2}\)