Space of modular forms of level 441 and weight 2

• Label: 441.2
• Level: 441
• Weight: 2
• Dimension: 5142
• Nonzero newspaces: 20
• Newform subspaces: 81
• Sturm bound: 28224
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 81 \)
Sturm bound:			\(28224\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(441))\).

	Total	New	Old
Modular forms	7536	5579	1957
Cusp forms	6577	5142	1435
Eisenstein series	959	437	522

Trace form

5142 * q - 45 * q^2 - 60 * q^3 - 37 * q^4 - 39 * q^5 - 60 * q^6 - 50 * q^7 - 63 * q^8 - 60 * q^9 - 105 * q^10 - 27 * q^11 - 84 * q^12 - 31 * q^13 - 60 * q^14 - 132 * q^15 - 69 * q^16 - 87 * q^17 - 108 * q^18 - 157 * q^19 - 135 * q^20 - 90 * q^21 - 117 * q^22 - 75 * q^23 - 132 * q^24 - 45 * q^25 - 111 * q^26 - 96 * q^27 - 156 * q^28 - 81 * q^29 - 144 * q^30 - 43 * q^31 - 141 * q^32 - 108 * q^33 - 87 * q^34 - 87 * q^35 - 228 * q^36 - 189 * q^37 - 213 * q^38 - 132 * q^39 - 285 * q^40 - 225 * q^41 - 138 * q^42 - 143 * q^43 - 321 * q^44 - 156 * q^45 - 363 * q^46 - 141 * q^47 - 36 * q^48 - 150 * q^49 - 246 * q^50 - 60 * q^51 - 233 * q^52 - 21 * q^53 - 198 * q^55 - 102 * q^56 - 12 * q^57 - 75 * q^58 + 87 * q^59 + 144 * q^60 - 68 * q^61 + 207 * q^62 + 12 * q^63 - 169 * q^64 + 81 * q^65 + 24 * q^66 - 39 * q^67 + 177 * q^68 - 12 * q^69 - 87 * q^70 - 93 * q^71 + 48 * q^72 - 217 * q^73 - 87 * q^74 - 84 * q^75 - 139 * q^76 - 99 * q^77 - 180 * q^78 - 135 * q^79 - 198 * q^80 - 228 * q^81 - 330 * q^82 - 279 * q^83 - 216 * q^84 - 249 * q^85 - 462 * q^86 - 240 * q^87 - 450 * q^88 - 411 * q^89 - 384 * q^90 - 311 * q^91 - 528 * q^92 - 288 * q^93 - 432 * q^94 - 459 * q^95 - 336 * q^96 - 280 * q^97 - 480 * q^98 - 384 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)

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
441.2.a	\(\chi_{441}(1, \cdot)\)	441.2.a.a	1	1
		441.2.a.b	1
		441.2.a.c	1
		441.2.a.d	1
		441.2.a.e	1
		441.2.a.f	1
		441.2.a.g	2
		441.2.a.h	2
		441.2.a.i	2
		441.2.a.j	2
441.2.c	\(\chi_{441}(440, \cdot)\)	441.2.c.a	4	1
		441.2.c.b	8
441.2.e	\(\chi_{441}(226, \cdot)\)	441.2.e.a	2	2
		441.2.e.b	2
		441.2.e.c	2
		441.2.e.d	2
		441.2.e.e	2
		441.2.e.f	4
		441.2.e.g	4
		441.2.e.h	4
		441.2.e.i	4
		441.2.e.j	4
441.2.f	\(\chi_{441}(148, \cdot)\)	441.2.f.a	2	2
		441.2.f.b	2
		441.2.f.c	6
		441.2.f.d	6
		441.2.f.e	10
		441.2.f.f	10
		441.2.f.g	12
		441.2.f.h	24
441.2.g	\(\chi_{441}(67, \cdot)\)	441.2.g.a	2	2
		441.2.g.b	6
		441.2.g.c	6
		441.2.g.d	6
		441.2.g.e	6
		441.2.g.f	10
		441.2.g.g	12
		441.2.g.h	24
441.2.h	\(\chi_{441}(214, \cdot)\)	441.2.h.a	2	2
		441.2.h.b	6
		441.2.h.c	6
		441.2.h.d	6
		441.2.h.e	6
		441.2.h.f	10
		441.2.h.g	12
		441.2.h.h	24
441.2.i	\(\chi_{441}(68, \cdot)\)	441.2.i.a	2	2
		441.2.i.b	10
		441.2.i.c	12
		441.2.i.d	48
441.2.o	\(\chi_{441}(146, \cdot)\)	441.2.o.a	2	2
		441.2.o.b	2
		441.2.o.c	10
		441.2.o.d	10
		441.2.o.e	48
441.2.p	\(\chi_{441}(80, \cdot)\)	441.2.p.a	4	2
		441.2.p.b	8
		441.2.p.c	16
441.2.s	\(\chi_{441}(362, \cdot)\)	441.2.s.a	2	2
		441.2.s.b	10
		441.2.s.c	12
		441.2.s.d	48
441.2.u	\(\chi_{441}(64, \cdot)\)	441.2.u.a	6	6
		441.2.u.b	12
		441.2.u.c	24
		441.2.u.d	36
		441.2.u.e	60
441.2.w	\(\chi_{441}(62, \cdot)\)	441.2.w.a	120	6
441.2.y	\(\chi_{441}(25, \cdot)\)	441.2.y.a	648	12
441.2.z	\(\chi_{441}(4, \cdot)\)	441.2.z.a	648	12
441.2.ba	\(\chi_{441}(22, \cdot)\)	441.2.ba.a	648	12
441.2.bb	\(\chi_{441}(37, \cdot)\)	441.2.bb.a	12	12
		441.2.bb.b	24
		441.2.bb.c	48
		441.2.bb.d	48
		441.2.bb.e	60
		441.2.bb.f	72
441.2.bd	\(\chi_{441}(47, \cdot)\)	441.2.bd.a	648	12
441.2.bg	\(\chi_{441}(17, \cdot)\)	441.2.bg.a	216	12
441.2.bh	\(\chi_{441}(20, \cdot)\)	441.2.bh.a	648	12
441.2.bn	\(\chi_{441}(5, \cdot)\)	441.2.bn.a	648	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

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