Space of modular forms of level 279 and weight 2

• Label: 279.2
• Level: 279
• Weight: 2
• Dimension: 2145
• Nonzero newspaces: 20
• Newform subspaces: 37
• Sturm bound: 11520
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 37 \)
Sturm bound:			\(11520\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(279))\).

	Total	New	Old
Modular forms	3120	2405	715
Cusp forms	2641	2145	496
Eisenstein series	479	260	219

Trace form

2145 * q - 45 * q^2 - 60 * q^3 - 45 * q^4 - 45 * q^5 - 60 * q^6 - 45 * q^7 - 45 * q^8 - 60 * q^9 - 135 * q^10 - 45 * q^11 - 60 * q^12 - 45 * q^13 - 45 * q^14 - 60 * q^15 - 45 * q^16 - 45 * q^17 - 60 * q^18 - 135 * q^19 - 45 * q^20 - 60 * q^21 - 75 * q^22 - 60 * q^23 - 60 * q^24 - 80 * q^25 - 75 * q^26 - 60 * q^27 - 215 * q^28 - 75 * q^29 - 60 * q^30 - 75 * q^31 - 180 * q^32 - 60 * q^33 - 105 * q^34 - 75 * q^35 - 60 * q^36 - 180 * q^37 - 75 * q^38 - 60 * q^39 - 105 * q^40 - 60 * q^41 - 60 * q^42 - 50 * q^43 - 45 * q^44 - 60 * q^45 - 135 * q^46 - 45 * q^47 - 60 * q^48 - 75 * q^49 - 120 * q^50 - 60 * q^51 - 120 * q^52 - 75 * q^53 - 60 * q^54 - 195 * q^55 - 180 * q^56 - 60 * q^57 - 150 * q^58 - 75 * q^59 - 150 * q^61 - 135 * q^62 - 120 * q^63 - 255 * q^64 - 135 * q^65 - 60 * q^66 - 75 * q^67 - 150 * q^68 - 60 * q^69 - 180 * q^70 - 105 * q^71 - 60 * q^72 - 165 * q^73 - 120 * q^74 - 30 * q^75 + 30 * q^76 + 60 * q^77 + 120 * q^78 + 60 * q^79 + 405 * q^80 + 60 * q^81 + 45 * q^82 + 270 * q^83 + 300 * q^84 + 135 * q^85 + 315 * q^86 + 60 * q^87 + 495 * q^88 + 180 * q^89 + 300 * q^90 + 60 * q^91 + 540 * q^92 + 180 * q^93 + 90 * q^94 + 315 * q^95 + 300 * q^96 + 150 * q^97 + 495 * q^98 + 90 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)

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
279.2.a	\(\chi_{279}(1, \cdot)\)	279.2.a.a	2	1
		279.2.a.b	2
		279.2.a.c	3
		279.2.a.d	6
279.2.c	\(\chi_{279}(278, \cdot)\)	279.2.c.a	12	1
279.2.e	\(\chi_{279}(160, \cdot)\)	279.2.e.a	60	2
279.2.f	\(\chi_{279}(94, \cdot)\)	279.2.f.a	30	2
		279.2.f.b	30
279.2.g	\(\chi_{279}(25, \cdot)\)	279.2.g.a	60	2
279.2.h	\(\chi_{279}(118, \cdot)\)	279.2.h.a	2	2
		279.2.h.b	4
		279.2.h.c	4
		279.2.h.d	6
		279.2.h.e	8
279.2.i	\(\chi_{279}(64, \cdot)\)	279.2.i.a	4	4
		279.2.i.b	8
		279.2.i.c	16
		279.2.i.d	24
279.2.j	\(\chi_{279}(26, \cdot)\)	279.2.j.a	4	2
		279.2.j.b	4
		279.2.j.c	12
279.2.o	\(\chi_{279}(212, \cdot)\)	279.2.o.a	60	2
279.2.r	\(\chi_{279}(68, \cdot)\)	279.2.r.a	60	2
279.2.s	\(\chi_{279}(92, \cdot)\)	279.2.s.a	60	2
279.2.w	\(\chi_{279}(89, \cdot)\)	279.2.w.a	48	4
279.2.y	\(\chi_{279}(10, \cdot)\)	279.2.y.a	8	8
		279.2.y.b	16
		279.2.y.c	16
		279.2.y.d	24
		279.2.y.e	32
279.2.z	\(\chi_{279}(4, \cdot)\)	279.2.z.a	240	8
279.2.ba	\(\chi_{279}(76, \cdot)\)	279.2.ba.a	240	8
279.2.bb	\(\chi_{279}(7, \cdot)\)	279.2.bb.a	240	8
279.2.be	\(\chi_{279}(65, \cdot)\)	279.2.be.a	240	8
279.2.bg	\(\chi_{279}(23, \cdot)\)	279.2.bg.a	240	8
279.2.bh	\(\chi_{279}(11, \cdot)\)	279.2.bh.a	240	8
279.2.bn	\(\chi_{279}(17, \cdot)\)	279.2.bn.a	80	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(279))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(279)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 2}\)