Space of modular forms of level 252 and weight 2

• Label: 252.2
• Level: 252
• Weight: 2
• Dimension: 718
• Nonzero newspaces: 20
• Newform subspaces: 40
• Sturm bound: 6912
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 40 \)
Sturm bound:			\(6912\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(252))\).

	Total	New	Old
Modular forms	1968	810	1158
Cusp forms	1489	718	771
Eisenstein series	479	92	387

Trace form

718 * q - 3 * q^2 + q^4 - 3 * q^5 - 6 * q^6 - q^7 - 15 * q^8 - 10 * q^10 + 9 * q^11 - 24 * q^12 + 10 * q^13 - 9 * q^14 - 6 * q^15 - 11 * q^16 - 9 * q^17 - 48 * q^18 + 29 * q^19 - 54 * q^20 - 3 * q^21 - 36 * q^22 + 27 * q^23 - 18 * q^24 + 36 * q^25 - 42 * q^26 + 18 * q^27 - 39 * q^28 - 6 * q^29 - 6 * q^30 + 5 * q^31 - 3 * q^32 - 78 * q^33 - 52 * q^34 - 51 * q^35 - 18 * q^36 - 69 * q^37 - 54 * q^38 - 30 * q^39 - 118 * q^40 - 162 * q^41 - 60 * q^42 - 74 * q^43 - 120 * q^44 - 102 * q^45 - 156 * q^46 - 81 * q^47 - 114 * q^48 - 71 * q^49 - 171 * q^50 - 72 * q^51 - 142 * q^52 - 87 * q^53 - 108 * q^54 - 54 * q^55 - 99 * q^56 - 108 * q^57 - 76 * q^58 - 45 * q^59 - 30 * q^60 + 7 * q^61 - 81 * q^63 - 59 * q^64 - 114 * q^65 + 54 * q^66 + 63 * q^67 + 84 * q^68 - 42 * q^69 + 102 * q^70 - 24 * q^71 + 96 * q^72 - 29 * q^73 + 210 * q^74 - 72 * q^75 + 144 * q^76 - 126 * q^77 + 84 * q^78 - 3 * q^79 + 198 * q^80 - 132 * q^81 + 80 * q^82 - 66 * q^83 + 66 * q^84 - 158 * q^85 + 126 * q^86 + 198 * q^88 - 201 * q^89 + 90 * q^90 - 10 * q^91 + 102 * q^92 - 144 * q^93 + 144 * q^94 + 3 * q^95 + 48 * q^96 - 158 * q^97 + 111 * q^98 + 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)

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
252.2.a	\(\chi_{252}(1, \cdot)\)	252.2.a.a	1	1
		252.2.a.b	1
252.2.b	\(\chi_{252}(55, \cdot)\)	252.2.b.a	2	1
		252.2.b.b	4
		252.2.b.c	4
		252.2.b.d	4
		252.2.b.e	4
252.2.e	\(\chi_{252}(71, \cdot)\)	252.2.e.a	12	1
252.2.f	\(\chi_{252}(125, \cdot)\)	252.2.f.a	4	1
252.2.i	\(\chi_{252}(25, \cdot)\)	252.2.i.a	2	2
		252.2.i.b	14
252.2.j	\(\chi_{252}(85, \cdot)\)	252.2.j.a	6	2
		252.2.j.b	6
252.2.k	\(\chi_{252}(37, \cdot)\)	252.2.k.a	2	2
		252.2.k.b	2
		252.2.k.c	2
252.2.l	\(\chi_{252}(193, \cdot)\)	252.2.l.a	2	2
		252.2.l.b	14
252.2.n	\(\chi_{252}(31, \cdot)\)	252.2.n.a	4	2
		252.2.n.b	84
252.2.o	\(\chi_{252}(95, \cdot)\)	252.2.o.a	88	2
252.2.t	\(\chi_{252}(17, \cdot)\)	252.2.t.a	4	2
252.2.w	\(\chi_{252}(5, \cdot)\)	252.2.w.a	16	2
252.2.x	\(\chi_{252}(41, \cdot)\)	252.2.x.a	16	2
252.2.ba	\(\chi_{252}(155, \cdot)\)	252.2.ba.a	72	2
252.2.bb	\(\chi_{252}(11, \cdot)\)	252.2.bb.a	88	2
252.2.be	\(\chi_{252}(107, \cdot)\)	252.2.be.a	32	2
252.2.bf	\(\chi_{252}(19, \cdot)\)	252.2.bf.a	4	2
		252.2.bf.b	4
		252.2.bf.c	4
		252.2.bf.d	4
		252.2.bf.e	4
		252.2.bf.f	8
		252.2.bf.g	8
252.2.bi	\(\chi_{252}(139, \cdot)\)	252.2.bi.a	4	2
		252.2.bi.b	4
		252.2.bi.c	80
252.2.bj	\(\chi_{252}(103, \cdot)\)	252.2.bj.a	4	2
		252.2.bj.b	84
252.2.bm	\(\chi_{252}(173, \cdot)\)	252.2.bm.a	16	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(252))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(252)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 2}\)