Space of modular forms of level 396 and weight 4

• Label: 396.4
• Level: 396
• Weight: 4
• Dimension: 5805
• Nonzero newspaces: 16
• Sturm bound: 34560
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(34560\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(396))\).

	Total	New	Old
Modular forms	13360	5969	7391
Cusp forms	12560	5805	6755
Eisenstein series	800	164	636

Trace form

5805 * q - 9 * q^2 + 6 * q^3 - 37 * q^4 - 66 * q^5 - 62 * q^6 - 14 * q^7 - 15 * q^8 - 130 * q^9 + 264 * q^10 + 35 * q^11 - 28 * q^12 - 154 * q^13 + 316 * q^14 + 360 * q^15 - 361 * q^16 + 280 * q^17 + 220 * q^18 - 85 * q^19 - 22 * q^20 + 452 * q^21 - 180 * q^22 + 404 * q^23 - 26 * q^24 + 358 * q^25 - 40 * q^26 - 1356 * q^27 - 216 * q^28 - 2116 * q^29 - 896 * q^30 - 274 * q^31 - 1404 * q^32 - 641 * q^33 - 948 * q^34 + 260 * q^35 - 2066 * q^36 - 1102 * q^37 - 1472 * q^38 + 372 * q^39 + 570 * q^40 - 642 * q^41 - 1564 * q^42 - 32 * q^43 + 1490 * q^44 - 1216 * q^45 + 234 * q^46 - 520 * q^47 + 2722 * q^48 + 4364 * q^49 + 2099 * q^50 + 1844 * q^51 - 2584 * q^52 + 2414 * q^53 + 662 * q^54 + 134 * q^55 - 28 * q^56 - 114 * q^57 + 402 * q^58 + 651 * q^59 + 7484 * q^60 - 4066 * q^61 + 11910 * q^62 + 928 * q^63 + 12299 * q^64 + 2820 * q^65 + 5316 * q^66 + 5652 * q^67 + 1800 * q^68 + 4176 * q^69 - 518 * q^70 + 4160 * q^71 - 7520 * q^72 + 3564 * q^73 - 15608 * q^74 - 3592 * q^75 - 6220 * q^76 - 8978 * q^77 - 14108 * q^78 - 8098 * q^79 - 15710 * q^80 - 19026 * q^81 - 10331 * q^82 - 10647 * q^83 + 8250 * q^84 - 3734 * q^85 + 20167 * q^86 - 628 * q^87 + 9294 * q^88 + 1178 * q^89 + 22384 * q^90 - 2772 * q^91 + 24078 * q^92 + 10312 * q^93 + 13654 * q^94 + 18978 * q^95 + 8050 * q^96 + 13977 * q^97 + 17534 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(396))\)

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
396.4.a	\(\chi_{396}(1, \cdot)\)	396.4.a.a	1	1
		396.4.a.b	1
		396.4.a.c	1
		396.4.a.d	1
		396.4.a.e	1
		396.4.a.f	1
		396.4.a.g	1
		396.4.a.h	2
		396.4.a.i	2
		396.4.a.j	2
396.4.b	\(\chi_{396}(197, \cdot)\)	396.4.b.a	6	1
		396.4.b.b	6
396.4.c	\(\chi_{396}(287, \cdot)\)	396.4.c.a	30	1
		396.4.c.b	30
396.4.h	\(\chi_{396}(307, \cdot)\)	396.4.h.a	4	1
		396.4.h.b	16
		396.4.h.c	32
		396.4.h.d	36
396.4.i	\(\chi_{396}(133, \cdot)\)	396.4.i.a	6	2
		396.4.i.b	22
		396.4.i.c	32
396.4.j	\(\chi_{396}(37, \cdot)\)	396.4.j.a	4	4
		396.4.j.b	8
		396.4.j.c	12
		396.4.j.d	12
		396.4.j.e	24
396.4.k	\(\chi_{396}(43, \cdot)\)	n/a	424	2
396.4.p	\(\chi_{396}(23, \cdot)\)	n/a	360	2
396.4.q	\(\chi_{396}(65, \cdot)\)	396.4.q.a	4	2
		396.4.q.b	4
		396.4.q.c	64
396.4.r	\(\chi_{396}(19, \cdot)\)	n/a	352	4
396.4.w	\(\chi_{396}(71, \cdot)\)	n/a	288	4
396.4.x	\(\chi_{396}(17, \cdot)\)	396.4.x.a	48	4
396.4.y	\(\chi_{396}(25, \cdot)\)	n/a	288	8
396.4.z	\(\chi_{396}(29, \cdot)\)	n/a	288	8
396.4.ba	\(\chi_{396}(47, \cdot)\)	n/a	1696	8
396.4.bf	\(\chi_{396}(7, \cdot)\)	n/a	1696	8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(396))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(396)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 2}\)