Space of modular forms of level 675 and weight 3

• Label: 675.3
• Level: 675
• Weight: 3
• Dimension: 23267
• Nonzero newspaces: 18
• Sturm bound: 97200
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(97200\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(675))\).

	Total	New	Old
Modular forms	33240	23923	9317
Cusp forms	31560	23267	8293
Eisenstein series	1680	656	1024

Trace form

23267 * q - 51 * q^2 - 78 * q^3 - 97 * q^4 - 64 * q^5 - 138 * q^6 - 95 * q^7 - 89 * q^8 - 72 * q^9 - 144 * q^10 - 131 * q^11 - 87 * q^12 - 123 * q^13 - 77 * q^14 - 96 * q^15 - 89 * q^16 + 15 * q^17 - 9 * q^18 - 6 * q^19 - 32 * q^20 + 12 * q^21 - 129 * q^22 + 72 * q^24 - 176 * q^25 - 352 * q^26 - 162 * q^27 - 302 * q^28 - 302 * q^29 - 96 * q^30 - 117 * q^31 + 477 * q^32 - 15 * q^33 + 795 * q^34 + 620 * q^35 + 672 * q^36 + 524 * q^37 + 1813 * q^38 + 543 * q^39 + 448 * q^40 + 841 * q^41 + 798 * q^42 + 87 * q^43 + 631 * q^44 - 156 * q^45 - 375 * q^46 - 549 * q^47 - 579 * q^48 - 1165 * q^49 - 1384 * q^50 - 876 * q^51 - 2089 * q^52 - 2328 * q^53 - 1566 * q^54 - 648 * q^55 - 3659 * q^56 - 1200 * q^57 - 1141 * q^58 - 1037 * q^59 - 528 * q^60 - 99 * q^61 + 308 * q^62 - 657 * q^63 + 1153 * q^64 + 944 * q^65 - 543 * q^66 + 1020 * q^67 + 2486 * q^68 + 27 * q^69 + 1040 * q^70 + 1003 * q^71 + 2184 * q^72 + 1757 * q^73 + 5223 * q^74 + 912 * q^75 + 2667 * q^76 + 4091 * q^77 + 3540 * q^78 + 1587 * q^79 + 1328 * q^80 + 1452 * q^81 + 1398 * q^82 + 1647 * q^83 + 1620 * q^84 - 496 * q^85 + 1429 * q^86 + 129 * q^87 - 2497 * q^88 - 1436 * q^89 - 324 * q^90 - 1211 * q^91 - 4683 * q^92 - 633 * q^93 - 3225 * q^94 - 1652 * q^95 - 2874 * q^96 - 2170 * q^97 - 6926 * q^98 - 1959 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(675))\)

We only show spaces with odd 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
675.3.c	\(\chi_{675}(26, \cdot)\)	675.3.c.a	1	1
		675.3.c.b	1
		675.3.c.c	1
		675.3.c.d	2
		675.3.c.e	2
		675.3.c.f	2
		675.3.c.g	2
		675.3.c.h	2
		675.3.c.i	2
		675.3.c.j	2
		675.3.c.k	2
		675.3.c.l	2
		675.3.c.m	2
		675.3.c.n	4
		675.3.c.o	4
		675.3.c.p	4
		675.3.c.q	4
		675.3.c.r	6
		675.3.c.s	6
675.3.d	\(\chi_{675}(674, \cdot)\)	675.3.d.a	2	1
		675.3.d.b	2
		675.3.d.c	2
		675.3.d.d	2
		675.3.d.e	4
		675.3.d.f	4
		675.3.d.g	4
		675.3.d.h	4
		675.3.d.i	4
		675.3.d.j	6
		675.3.d.k	6
		675.3.d.l	8
675.3.g	\(\chi_{675}(82, \cdot)\)	675.3.g.a	4	2
		675.3.g.b	4
		675.3.g.c	4
		675.3.g.d	4
		675.3.g.e	8
		675.3.g.f	8
		675.3.g.g	8
		675.3.g.h	12
		675.3.g.i	12
		675.3.g.j	16
		675.3.g.k	16
675.3.i	\(\chi_{675}(224, \cdot)\)	675.3.i.a	4	2
		675.3.i.b	32
		675.3.i.c	32
675.3.j	\(\chi_{675}(251, \cdot)\)	675.3.j.a	2	2
		675.3.j.b	16
		675.3.j.c	16
		675.3.j.d	16
		675.3.j.e	20
675.3.m	\(\chi_{675}(134, \cdot)\)	n/a	320	4
675.3.o	\(\chi_{675}(161, \cdot)\)	n/a	320	4
675.3.p	\(\chi_{675}(118, \cdot)\)	n/a	136	4
675.3.s	\(\chi_{675}(74, \cdot)\)	n/a	636	6
675.3.t	\(\chi_{675}(101, \cdot)\)	n/a	666	6
675.3.v	\(\chi_{675}(28, \cdot)\)	n/a	640	8
675.3.x	\(\chi_{675}(71, \cdot)\)	n/a	464	8
675.3.z	\(\chi_{675}(44, \cdot)\)	n/a	464	8
675.3.bb	\(\chi_{675}(7, \cdot)\)	n/a	1272	12
675.3.be	\(\chi_{675}(37, \cdot)\)	n/a	928	16
675.3.bf	\(\chi_{675}(11, \cdot)\)	n/a	4272	24
675.3.bh	\(\chi_{675}(14, \cdot)\)	n/a	4272	24
675.3.bj	\(\chi_{675}(13, \cdot)\)	n/a	8544	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(675)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)