Space of modular forms of level 445 and weight 2

• Label: 445.2
• Level: 445
• Weight: 2
• Dimension: 6995
• Nonzero newspaces: 16
• Newform subspaces: 32
• Sturm bound: 31680
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 445 = 5 \cdot 89 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(31680\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(445))\).

	Total	New	Old
Modular forms	8272	7519	753
Cusp forms	7569	6995	574
Eisenstein series	703	524	179

Trace form

6995 * q - 91 * q^2 - 92 * q^3 - 95 * q^4 - 133 * q^5 - 276 * q^6 - 96 * q^7 - 103 * q^8 - 101 * q^9 - 135 * q^10 - 276 * q^11 - 116 * q^12 - 102 * q^13 - 112 * q^14 - 136 * q^15 - 295 * q^16 - 106 * q^17 - 127 * q^18 - 108 * q^19 - 139 * q^20 - 296 * q^21 - 124 * q^22 - 112 * q^23 - 148 * q^24 - 133 * q^25 - 306 * q^26 - 128 * q^27 - 144 * q^28 - 118 * q^29 - 144 * q^30 - 296 * q^31 - 151 * q^32 - 136 * q^33 - 142 * q^34 - 140 * q^35 - 355 * q^36 - 126 * q^37 - 148 * q^38 - 144 * q^39 - 147 * q^40 - 306 * q^41 - 184 * q^42 - 132 * q^43 - 172 * q^44 - 145 * q^45 - 336 * q^46 - 136 * q^47 - 212 * q^48 - 145 * q^49 - 135 * q^50 - 336 * q^51 - 186 * q^52 - 142 * q^53 - 208 * q^54 - 144 * q^55 - 384 * q^56 - 168 * q^57 - 178 * q^58 - 148 * q^59 - 160 * q^60 - 326 * q^61 - 184 * q^62 - 192 * q^63 - 215 * q^64 - 146 * q^65 - 408 * q^66 - 156 * q^67 - 214 * q^68 - 184 * q^69 - 156 * q^70 - 336 * q^71 - 19 * q^72 - 74 * q^73 + 18 * q^74 + 84 * q^75 + 124 * q^76 - 8 * q^77 + 272 * q^78 + 8 * q^79 + 167 * q^80 + 55 * q^81 + 138 * q^82 + 92 * q^83 + 920 * q^84 - 18 * q^85 - 44 * q^86 + 232 * q^87 + 348 * q^88 + 175 * q^89 + 225 * q^90 - 24 * q^91 + 272 * q^92 + 224 * q^93 + 120 * q^94 - 20 * q^95 + 716 * q^96 + 78 * q^97 + 93 * q^98 + 196 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)

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
445.2.a	\(\chi_{445}(1, \cdot)\)	445.2.a.a	2	1
		445.2.a.b	2
		445.2.a.c	2
		445.2.a.d	4
		445.2.a.e	4
		445.2.a.f	7
		445.2.a.g	8
445.2.b	\(\chi_{445}(179, \cdot)\)	445.2.b.a	6	1
		445.2.b.b	10
		445.2.b.c	28
445.2.c	\(\chi_{445}(444, \cdot)\)	445.2.c.a	44	1
445.2.d	\(\chi_{445}(266, \cdot)\)	445.2.d.a	2	1
		445.2.d.b	12
		445.2.d.c	16
445.2.e	\(\chi_{445}(34, \cdot)\)	445.2.e.a	84	2
445.2.j	\(\chi_{445}(301, \cdot)\)	445.2.j.a	2	2
		445.2.j.b	2
		445.2.j.c	24
		445.2.j.d	32
445.2.l	\(\chi_{445}(12, \cdot)\)	445.2.l.a	172	4
445.2.m	\(\chi_{445}(37, \cdot)\)	445.2.m.a	172	4
445.2.o	\(\chi_{445}(16, \cdot)\)	445.2.o.a	140	10
		445.2.o.b	160
445.2.p	\(\chi_{445}(11, \cdot)\)	445.2.p.a	140	10
		445.2.p.b	160
445.2.q	\(\chi_{445}(44, \cdot)\)	445.2.q.a	440	10
445.2.r	\(\chi_{445}(4, \cdot)\)	445.2.r.a	440	10
445.2.s	\(\chi_{445}(21, \cdot)\)	445.2.s.a	280	20
		445.2.s.b	320
445.2.x	\(\chi_{445}(9, \cdot)\)	445.2.x.a	840	20
445.2.z	\(\chi_{445}(3, \cdot)\)	445.2.z.a	1720	40
445.2.ba	\(\chi_{445}(7, \cdot)\)	445.2.ba.a	1720	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 2}\)