Space of modular forms of level 441 and weight 3

• Label: 441.3
• Level: 441
• Weight: 3
• Dimension: 10502
• Nonzero newspaces: 20
• Newform subspaces: 83
• Sturm bound: 42336
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 83 \)
Sturm bound:			\(42336\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(441))\).

	Total	New	Old
Modular forms	14592	10938	3654
Cusp forms	13632	10502	3130
Eisenstein series	960	436	524

Trace form

10502 * q - 48 * q^2 - 63 * q^3 - 62 * q^4 - 45 * q^5 - 51 * q^6 - 50 * q^7 - 87 * q^8 - 69 * q^9 - 153 * q^10 - 42 * q^11 - 6 * q^12 + 9 * q^13 + 66 * q^14 + 12 * q^15 + 302 * q^16 + 165 * q^17 + 36 * q^18 - 63 * q^19 - 33 * q^20 - 90 * q^21 - 318 * q^22 - 351 * q^23 - 393 * q^24 - 394 * q^25 - 531 * q^26 - 258 * q^27 - 450 * q^28 - 339 * q^29 + 18 * q^30 + 309 * q^31 + 582 * q^32 + 333 * q^33 + 930 * q^34 + 375 * q^35 + 483 * q^36 + 559 * q^37 + 1056 * q^38 + 60 * q^39 + 1323 * q^40 + 246 * q^41 - 138 * q^42 - 130 * q^43 - 375 * q^44 - 498 * q^45 - 885 * q^46 - 957 * q^47 - 1731 * q^48 - 444 * q^49 - 2871 * q^50 - 1491 * q^51 - 1447 * q^52 - 1941 * q^53 - 2025 * q^54 - 1224 * q^55 - 2034 * q^56 - 621 * q^57 - 813 * q^58 - 606 * q^59 - 702 * q^60 - 652 * q^61 - 651 * q^62 + 12 * q^63 - 983 * q^64 + 825 * q^65 + 1014 * q^66 + 268 * q^67 + 2682 * q^68 + 1788 * q^69 + 711 * q^70 + 2415 * q^71 + 3927 * q^72 + 1221 * q^73 + 3711 * q^74 + 2613 * q^75 + 834 * q^76 + 1035 * q^77 + 2304 * q^78 + 655 * q^79 + 3540 * q^80 + 195 * q^81 + 1860 * q^82 + 1065 * q^83 + 36 * q^84 + 285 * q^85 + 1203 * q^86 - 258 * q^87 + 2487 * q^88 + 405 * q^89 - 258 * q^90 + 67 * q^91 + 942 * q^92 - 384 * q^93 - 648 * q^94 - 1377 * q^95 - 1020 * q^96 - 1371 * q^97 - 1320 * q^98 - 1248 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(441))\)

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
441.3.b	\(\chi_{441}(197, \cdot)\)	441.3.b.a	4	1
		441.3.b.b	4
		441.3.b.c	6
		441.3.b.d	6
		441.3.b.e	8
441.3.d	\(\chi_{441}(244, \cdot)\)	441.3.d.a	2	1
		441.3.d.b	2
		441.3.d.c	2
		441.3.d.d	2
		441.3.d.e	4
		441.3.d.f	4
		441.3.d.g	8
		441.3.d.h	8
441.3.j	\(\chi_{441}(263, \cdot)\)	441.3.j.a	2	2
		441.3.j.b	2
		441.3.j.c	6
		441.3.j.d	8
		441.3.j.e	16
		441.3.j.f	22
		441.3.j.g	24
		441.3.j.h	24
		441.3.j.i	48
441.3.k	\(\chi_{441}(31, \cdot)\)	441.3.k.a	28	2
		441.3.k.b	28
		441.3.k.c	96
441.3.l	\(\chi_{441}(97, \cdot)\)	441.3.l.a	28	2
		441.3.l.b	28
		441.3.l.c	96
441.3.m	\(\chi_{441}(19, \cdot)\)	441.3.m.a	2	2
		441.3.m.b	2
		441.3.m.c	2
		441.3.m.d	2
		441.3.m.e	2
		441.3.m.f	2
		441.3.m.g	2
		441.3.m.h	4
		441.3.m.i	4
		441.3.m.j	8
		441.3.m.k	8
		441.3.m.l	8
		441.3.m.m	16
441.3.n	\(\chi_{441}(128, \cdot)\)	441.3.n.a	2	2
		441.3.n.b	2
		441.3.n.c	6
		441.3.n.d	8
		441.3.n.e	16
		441.3.n.f	22
		441.3.n.g	24
		441.3.n.h	24
		441.3.n.i	48
441.3.q	\(\chi_{441}(116, \cdot)\)	441.3.q.a	8	2
		441.3.q.b	8
		441.3.q.c	8
		441.3.q.d	12
		441.3.q.e	16
441.3.r	\(\chi_{441}(50, \cdot)\)	441.3.r.a	2	2
		441.3.r.b	6
		441.3.r.c	6
		441.3.r.d	8
		441.3.r.e	16
		441.3.r.f	22
		441.3.r.g	22
		441.3.r.h	24
		441.3.r.i	48
441.3.t	\(\chi_{441}(166, \cdot)\)	441.3.t.a	28	2
		441.3.t.b	28
		441.3.t.c	96
441.3.v	\(\chi_{441}(55, \cdot)\)	441.3.v.a	54	6
		441.3.v.b	108
		441.3.v.c	108
441.3.x	\(\chi_{441}(8, \cdot)\)	441.3.x.a	216	6
441.3.bc	\(\chi_{441}(40, \cdot)\)	441.3.bc.a	1320	12
441.3.be	\(\chi_{441}(29, \cdot)\)	441.3.be.a	1320	12
441.3.bf	\(\chi_{441}(44, \cdot)\)	441.3.bf.a	456	12
441.3.bi	\(\chi_{441}(2, \cdot)\)	441.3.bi.a	1320	12
441.3.bj	\(\chi_{441}(10, \cdot)\)	441.3.bj.a	12	12
		441.3.bj.b	96
		441.3.bj.c	108
		441.3.bj.d	120
		441.3.bj.e	216
441.3.bk	\(\chi_{441}(13, \cdot)\)	441.3.bk.a	1320	12
441.3.bl	\(\chi_{441}(61, \cdot)\)	441.3.bl.a	1320	12
441.3.bm	\(\chi_{441}(11, \cdot)\)	441.3.bm.a	1320	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)