Space of modular forms of level 361 and weight 4

• Label: 361.4
• Level: 361
• Weight: 4
• Dimension: 15921
• Nonzero newspaces: 6
• Sturm bound: 43320
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 361 = 19^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(43320\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(361))\).

	Total	New	Old
Modular forms	16497	16390	107
Cusp forms	15993	15921	72
Eisenstein series	504	469	35

Trace form

15921 * q - 153 * q^2 - 153 * q^3 - 153 * q^4 - 153 * q^5 - 153 * q^6 - 153 * q^7 - 153 * q^8 - 153 * q^9 - 153 * q^10 - 153 * q^11 + 423 * q^12 + 135 * q^13 - 81 * q^14 - 369 * q^15 - 1017 * q^16 - 441 * q^17 - 1107 * q^18 - 540 * q^19 - 1449 * q^20 - 657 * q^21 - 477 * q^22 - 117 * q^23 + 711 * q^24 + 711 * q^25 + 1215 * q^26 + 2457 * q^27 + 4437 * q^28 + 1107 * q^29 + 2241 * q^30 + 27 * q^31 - 783 * q^32 - 1989 * q^33 - 2403 * q^34 - 2385 * q^35 - 6309 * q^36 - 1467 * q^37 - 2493 * q^38 - 4077 * q^39 - 3915 * q^40 - 1053 * q^41 - 3213 * q^42 + 99 * q^43 + 5697 * q^44 + 6003 * q^45 + 6885 * q^46 + 3591 * q^47 + 11061 * q^48 + 3267 * q^49 + 4257 * q^50 + 117 * q^51 - 4905 * q^52 - 3321 * q^53 - 5067 * q^54 - 4041 * q^55 - 12231 * q^56 - 2682 * q^57 - 4185 * q^58 - 4653 * q^59 - 3231 * q^60 + 5355 * q^61 + 6669 * q^62 + 6615 * q^63 + 8055 * q^64 + 5067 * q^65 + 6903 * q^66 + 1683 * q^67 + 7029 * q^68 + 495 * q^69 - 801 * q^70 + 4203 * q^71 - 6075 * q^72 - 10035 * q^73 - 10521 * q^74 - 12735 * q^75 - 6912 * q^76 - 9621 * q^77 + 387 * q^78 - 5481 * q^79 + 5607 * q^80 - 1107 * q^81 - 4599 * q^82 + 531 * q^83 + 2655 * q^84 + 1719 * q^85 + 2673 * q^86 + 2583 * q^87 + 2151 * q^88 + 7947 * q^89 + 8217 * q^90 + 9783 * q^91 + 4905 * q^92 + 459 * q^93 + 5553 * q^94 + 5544 * q^95 + 999 * q^96 + 6543 * q^97 + 13185 * q^98 + 1413 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(361))\)

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
361.4.a	\(\chi_{361}(1, \cdot)\)	361.4.a.a	1	1
		361.4.a.b	1
		361.4.a.c	2
		361.4.a.d	2
		361.4.a.e	2
		361.4.a.f	2
		361.4.a.g	2
		361.4.a.h	2
		361.4.a.i	3
		361.4.a.j	4
		361.4.a.k	6
		361.4.a.l	6
		361.4.a.m	12
		361.4.a.n	12
		361.4.a.o	20
361.4.c	\(\chi_{361}(68, \cdot)\)	n/a	154	2
361.4.e	\(\chi_{361}(28, \cdot)\)	n/a	462	6
361.4.g	\(\chi_{361}(20, \cdot)\)	n/a	1692	18
361.4.i	\(\chi_{361}(7, \cdot)\)	n/a	3384	36
361.4.k	\(\chi_{361}(4, \cdot)\)	n/a	10152	108

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(361))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(361)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)