Space of modular forms of level 891 and weight 2

• Label: 891.2
• Level: 891
• Weight: 2
• Dimension: 22152
• Nonzero newspaces: 16
• Newform subspaces: 89
• Sturm bound: 116640
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 89 \)
Sturm bound:			\(116640\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(891))\).

	Total	New	Old
Modular forms	30240	23160	7080
Cusp forms	28081	22152	5929
Eisenstein series	2159	1008	1151

Trace form

22152 * q - 96 * q^2 - 144 * q^3 - 156 * q^4 - 90 * q^5 - 144 * q^6 - 154 * q^7 - 72 * q^8 - 144 * q^9 - 212 * q^10 - 99 * q^11 - 324 * q^12 - 142 * q^13 - 54 * q^14 - 144 * q^15 - 156 * q^16 - 66 * q^17 - 162 * q^18 - 244 * q^19 - 162 * q^20 - 198 * q^21 - 185 * q^22 - 282 * q^23 - 252 * q^24 - 180 * q^25 - 270 * q^26 - 198 * q^27 - 280 * q^28 - 150 * q^29 - 252 * q^30 - 178 * q^31 - 192 * q^32 - 189 * q^33 - 382 * q^34 - 114 * q^35 - 216 * q^36 - 208 * q^37 - 18 * q^38 - 144 * q^39 - 206 * q^40 - 90 * q^41 - 234 * q^42 - 154 * q^43 - 171 * q^44 - 432 * q^45 - 320 * q^46 - 222 * q^47 - 342 * q^48 - 200 * q^49 - 384 * q^50 - 270 * q^51 - 238 * q^52 - 246 * q^53 - 396 * q^54 - 305 * q^55 - 558 * q^56 - 252 * q^57 - 206 * q^58 - 234 * q^59 - 378 * q^60 - 190 * q^61 - 306 * q^62 - 252 * q^63 - 298 * q^64 - 114 * q^65 - 162 * q^66 - 378 * q^67 + 96 * q^68 - 36 * q^69 - 242 * q^70 + 114 * q^71 + 288 * q^72 - 154 * q^73 + 270 * q^74 + 36 * q^75 - 202 * q^76 + 57 * q^77 - 90 * q^78 - 154 * q^79 + 300 * q^80 - 380 * q^82 + 48 * q^83 + 306 * q^84 - 338 * q^85 + 96 * q^86 + 144 * q^87 - 473 * q^88 - 210 * q^89 + 18 * q^90 - 342 * q^91 - 270 * q^92 - 180 * q^93 - 482 * q^94 - 462 * q^95 - 126 * q^96 - 382 * q^97 - 672 * q^98 - 234 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)

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
891.2.a	\(\chi_{891}(1, \cdot)\)	891.2.a.a	1	1
		891.2.a.b	1
		891.2.a.c	1
		891.2.a.d	1
		891.2.a.e	1
		891.2.a.f	1
		891.2.a.g	1
		891.2.a.h	1
		891.2.a.i	2
		891.2.a.j	2
		891.2.a.k	3
		891.2.a.l	3
		891.2.a.m	3
		891.2.a.n	3
		891.2.a.o	4
		891.2.a.p	4
		891.2.a.q	4
		891.2.a.r	4
891.2.d	\(\chi_{891}(890, \cdot)\)	891.2.d.a	4	1
		891.2.d.b	16
		891.2.d.c	24
891.2.e	\(\chi_{891}(298, \cdot)\)	891.2.e.a	2	2
		891.2.e.b	2
		891.2.e.c	2
		891.2.e.d	2
		891.2.e.e	2
		891.2.e.f	2
		891.2.e.g	2
		891.2.e.h	2
		891.2.e.i	2
		891.2.e.j	2
		891.2.e.k	2
		891.2.e.l	2
		891.2.e.m	4
		891.2.e.n	4
		891.2.e.o	4
		891.2.e.p	4
		891.2.e.q	6
		891.2.e.r	6
		891.2.e.s	6
		891.2.e.t	6
		891.2.e.u	8
		891.2.e.v	8
891.2.f	\(\chi_{891}(82, \cdot)\)	891.2.f.a	4	4
		891.2.f.b	4
		891.2.f.c	24
		891.2.f.d	24
		891.2.f.e	36
		891.2.f.f	36
		891.2.f.g	48
891.2.g	\(\chi_{891}(296, \cdot)\)	891.2.g.a	4	2
		891.2.g.b	8
		891.2.g.c	8
		891.2.g.d	8
		891.2.g.e	16
		891.2.g.f	48
891.2.j	\(\chi_{891}(100, \cdot)\)	891.2.j.a	6	6
		891.2.j.b	72
		891.2.j.c	102
891.2.k	\(\chi_{891}(161, \cdot)\)	891.2.k.a	80	4
		891.2.k.b	96
891.2.n	\(\chi_{891}(136, \cdot)\)	891.2.n.a	8	8
		891.2.n.b	8
		891.2.n.c	8
		891.2.n.d	8
		891.2.n.e	16
		891.2.n.f	32
		891.2.n.g	32
		891.2.n.h	32
		891.2.n.i	32
		891.2.n.j	48
		891.2.n.k	48
		891.2.n.l	96
891.2.o	\(\chi_{891}(98, \cdot)\)	891.2.o.a	12	6
		891.2.o.b	192
891.2.r	\(\chi_{891}(34, \cdot)\)	891.2.r.a	774	18
		891.2.r.b	846
891.2.u	\(\chi_{891}(107, \cdot)\)	891.2.u.a	16	8
		891.2.u.b	32
		891.2.u.c	32
		891.2.u.d	32
		891.2.u.e	64
		891.2.u.f	192
891.2.v	\(\chi_{891}(37, \cdot)\)	891.2.v.a	816	24
891.2.y	\(\chi_{891}(32, \cdot)\)	891.2.y.a	36	18
		891.2.y.b	1872
891.2.bb	\(\chi_{891}(8, \cdot)\)	891.2.bb.a	816	24
891.2.bc	\(\chi_{891}(4, \cdot)\)	891.2.bc.a	7632	72
891.2.bd	\(\chi_{891}(2, \cdot)\)	891.2.bd.a	7632	72

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(891))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(891)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)