Space of modular forms of level 675 and weight 2

• Label: 675.2
• Level: 675
• Weight: 2
• Dimension: 11469
• Nonzero newspaces: 18
• Newform subspaces: 76
• Sturm bound: 64800
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 76 \)
Sturm bound:			\(64800\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(675))\).

	Total	New	Old
Modular forms	17040	12125	4915
Cusp forms	15361	11469	3892
Eisenstein series	1679	656	1023

Trace form

11469 * q - 54 * q^2 - 78 * q^3 - 92 * q^4 - 64 * q^5 - 120 * q^6 - 91 * q^7 - 26 * q^8 - 72 * q^9 - 104 * q^10 - 61 * q^11 - 60 * q^12 - 69 * q^13 + 7 * q^14 - 96 * q^15 - 104 * q^16 - 15 * q^17 - 63 * q^18 - 78 * q^19 - 32 * q^20 - 132 * q^21 - 33 * q^22 - 20 * q^23 - 90 * q^24 - 96 * q^25 - 126 * q^26 - 81 * q^27 - 170 * q^28 + 2 * q^29 - 96 * q^30 - 109 * q^31 - 112 * q^32 - 96 * q^33 - 75 * q^34 - 100 * q^35 - 246 * q^36 - 92 * q^37 - 174 * q^38 - 159 * q^39 - 192 * q^40 - 209 * q^41 - 246 * q^42 - 201 * q^43 - 421 * q^44 - 156 * q^45 - 223 * q^46 - 231 * q^47 - 327 * q^48 - 158 * q^49 - 184 * q^50 - 354 * q^51 - 197 * q^52 - 186 * q^53 - 270 * q^54 - 248 * q^55 - 241 * q^56 - 147 * q^57 - 63 * q^58 - 8 * q^59 - 168 * q^60 - 73 * q^61 + 4 * q^62 - 63 * q^63 - 144 * q^64 - 96 * q^65 - 129 * q^66 - 78 * q^67 - 223 * q^68 - 63 * q^69 - 240 * q^70 + 11 * q^71 - 246 * q^72 - 149 * q^73 - 371 * q^74 - 168 * q^75 - 506 * q^76 - 393 * q^77 - 366 * q^78 - 333 * q^79 - 552 * q^80 - 276 * q^81 - 684 * q^82 - 493 * q^83 - 522 * q^84 - 256 * q^85 - 757 * q^86 - 303 * q^87 - 546 * q^88 - 579 * q^89 - 324 * q^90 - 371 * q^91 - 847 * q^92 - 399 * q^93 - 387 * q^94 - 212 * q^95 - 552 * q^96 - 212 * q^97 - 725 * q^98 - 339 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(675))\)

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
675.2.a	\(\chi_{675}(1, \cdot)\)	675.2.a.a	1	1
		675.2.a.b	1
		675.2.a.c	1
		675.2.a.d	1
		675.2.a.e	1
		675.2.a.f	1
		675.2.a.g	1
		675.2.a.h	1
		675.2.a.i	1
		675.2.a.j	2
		675.2.a.k	2
		675.2.a.l	2
		675.2.a.m	2
		675.2.a.n	2
		675.2.a.o	2
		675.2.a.p	2
		675.2.a.q	2
675.2.b	\(\chi_{675}(649, \cdot)\)	675.2.b.a	2	1
		675.2.b.b	2
		675.2.b.c	2
		675.2.b.d	2
		675.2.b.e	2
		675.2.b.f	2
		675.2.b.g	4
		675.2.b.h	4
		675.2.b.i	4
675.2.e	\(\chi_{675}(226, \cdot)\)	675.2.e.a	2	2
		675.2.e.b	6
		675.2.e.c	8
		675.2.e.d	8
		675.2.e.e	8
675.2.f	\(\chi_{675}(107, \cdot)\)	675.2.f.a	4	2
		675.2.f.b	4
		675.2.f.c	4
		675.2.f.d	4
		675.2.f.e	4
		675.2.f.f	4
		675.2.f.g	8
		675.2.f.h	8
		675.2.f.i	8
675.2.h	\(\chi_{675}(136, \cdot)\)	675.2.h.a	40	4
		675.2.h.b	40
		675.2.h.c	40
		675.2.h.d	40
675.2.k	\(\chi_{675}(199, \cdot)\)	675.2.k.a	4	2
		675.2.k.b	12
		675.2.k.c	16
675.2.l	\(\chi_{675}(76, \cdot)\)	675.2.l.a	6	6
		675.2.l.b	6
		675.2.l.c	12
		675.2.l.d	30
		675.2.l.e	42
		675.2.l.f	66
		675.2.l.g	66
		675.2.l.h	96
675.2.n	\(\chi_{675}(109, \cdot)\)	675.2.n.a	80	4
		675.2.n.b	80
675.2.q	\(\chi_{675}(143, \cdot)\)	675.2.q.a	16	4
		675.2.q.b	16
		675.2.q.c	32
675.2.r	\(\chi_{675}(46, \cdot)\)	675.2.r.a	224	8
675.2.u	\(\chi_{675}(49, \cdot)\)	675.2.u.a	12	6
		675.2.u.b	24
		675.2.u.c	60
		675.2.u.d	84
		675.2.u.e	132
675.2.w	\(\chi_{675}(53, \cdot)\)	675.2.w.a	160	8
		675.2.w.b	160
675.2.y	\(\chi_{675}(19, \cdot)\)	675.2.y.a	224	8
675.2.ba	\(\chi_{675}(32, \cdot)\)	675.2.ba.a	144	12
		675.2.ba.b	192
		675.2.ba.c	288
675.2.bc	\(\chi_{675}(16, \cdot)\)	675.2.bc.a	2112	24
675.2.bd	\(\chi_{675}(8, \cdot)\)	675.2.bd.a	448	16
675.2.bg	\(\chi_{675}(4, \cdot)\)	675.2.bg.a	2112	24
675.2.bi	\(\chi_{675}(2, \cdot)\)	675.2.bi.a	4224	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(675))\) into lower level spaces

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