Space of modular forms of level 552 and weight 2

• Label: 552.2
• Level: 552
• Weight: 2
• Dimension: 3466
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 33792
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(33792\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(552))\).

	Total	New	Old
Modular forms	8976	3634	5342
Cusp forms	7921	3466	4455
Eisenstein series	1055	168	887

Trace form

3466 * q + 4 * q^2 - 16 * q^3 - 36 * q^4 + 4 * q^5 - 26 * q^6 - 36 * q^7 - 8 * q^8 - 38 * q^9 - 52 * q^10 - 8 * q^11 - 38 * q^12 + 4 * q^13 - 8 * q^14 - 34 * q^15 - 44 * q^16 + 4 * q^17 - 10 * q^18 - 44 * q^19 + 16 * q^20 - 28 * q^22 - 20 * q^24 - 70 * q^25 + 16 * q^26 - 40 * q^27 - 44 * q^28 - 12 * q^29 - 14 * q^30 - 68 * q^31 - 16 * q^32 - 52 * q^33 - 84 * q^34 + 44 * q^35 - 30 * q^36 + 76 * q^37 - 16 * q^38 + 34 * q^39 - 60 * q^40 + 48 * q^41 - 30 * q^42 + 76 * q^43 + 4 * q^45 - 36 * q^46 + 136 * q^47 - 6 * q^48 + 42 * q^49 + 4 * q^50 + 58 * q^51 - 76 * q^52 + 48 * q^53 - 34 * q^54 + 60 * q^55 + 16 * q^56 - 16 * q^57 - 20 * q^58 + 36 * q^59 - 22 * q^60 + 4 * q^61 + 8 * q^62 - 30 * q^63 - 12 * q^64 - 40 * q^65 - 104 * q^66 - 92 * q^67 - 8 * q^69 - 72 * q^70 - 64 * q^71 - 46 * q^72 - 92 * q^73 - 76 * q^74 - 110 * q^75 - 216 * q^76 - 258 * q^78 - 200 * q^79 - 396 * q^80 - 154 * q^81 - 236 * q^82 - 124 * q^83 - 314 * q^84 - 124 * q^85 - 424 * q^86 - 184 * q^87 - 428 * q^88 - 80 * q^89 - 432 * q^90 - 352 * q^91 - 396 * q^92 + 16 * q^93 - 488 * q^94 - 248 * q^95 - 488 * q^96 - 176 * q^97 - 364 * q^98 - 196 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(552))\)

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
552.2.a	\(\chi_{552}(1, \cdot)\)	552.2.a.a	1	1
		552.2.a.b	1
		552.2.a.c	1
		552.2.a.d	1
		552.2.a.e	1
		552.2.a.f	2
		552.2.a.g	3
552.2.b	\(\chi_{552}(413, \cdot)\)	552.2.b.a	6	1
		552.2.b.b	6
		552.2.b.c	80
552.2.e	\(\chi_{552}(47, \cdot)\)	None	0	1
552.2.f	\(\chi_{552}(277, \cdot)\)	552.2.f.a	2	1
		552.2.f.b	4
		552.2.f.c	18
		552.2.f.d	20
552.2.i	\(\chi_{552}(367, \cdot)\)	None	0	1
552.2.j	\(\chi_{552}(323, \cdot)\)	552.2.j.a	2	1
		552.2.j.b	2
		552.2.j.c	42
		552.2.j.d	42
552.2.m	\(\chi_{552}(137, \cdot)\)	552.2.m.a	8	1
		552.2.m.b	16
552.2.n	\(\chi_{552}(91, \cdot)\)	552.2.n.a	24	1
		552.2.n.b	24
552.2.q	\(\chi_{552}(25, \cdot)\)	552.2.q.a	30	10
		552.2.q.b	30
		552.2.q.c	30
		552.2.q.d	30
552.2.t	\(\chi_{552}(19, \cdot)\)	552.2.t.a	240	10
		552.2.t.b	240
552.2.u	\(\chi_{552}(17, \cdot)\)	552.2.u.a	240	10
552.2.x	\(\chi_{552}(35, \cdot)\)	552.2.x.a	920	10
552.2.y	\(\chi_{552}(7, \cdot)\)	None	0	10
552.2.bb	\(\chi_{552}(13, \cdot)\)	552.2.bb.a	480	10
552.2.bc	\(\chi_{552}(71, \cdot)\)	None	0	10
552.2.bf	\(\chi_{552}(5, \cdot)\)	552.2.bf.a	920	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(552))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(552)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 2}\)