Space of modular forms of level 1452 and weight 3

• Label: 1452.3
• Level: 1452
• Weight: 3
• Dimension: 49703
• Nonzero newspaces: 16
• Sturm bound: 348480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(348480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1452))\).

	Total	New	Old
Modular forms	117760	50263	67497
Cusp forms	114560	49703	64857
Eisenstein series	3200	560	2640

Trace form

49703 * q - 2 * q^2 - 3 * q^3 - 94 * q^4 - 4 * q^5 - 39 * q^6 + 62 * q^7 + 16 * q^8 - 67 * q^9 - 106 * q^10 - 10 * q^11 - 97 * q^12 - 258 * q^13 - 164 * q^14 - 220 * q^15 - 506 * q^16 - 280 * q^17 - 99 * q^18 - 94 * q^19 - 92 * q^20 - 92 * q^21 - 40 * q^22 + 80 * q^23 + 135 * q^24 + 123 * q^25 + 496 * q^26 - 177 * q^27 + 658 * q^28 + 268 * q^29 + 393 * q^30 + 354 * q^31 + 408 * q^32 - 225 * q^33 + 530 * q^34 - 320 * q^35 + 527 * q^36 - 1062 * q^37 + 572 * q^38 + 116 * q^39 + 298 * q^40 - 124 * q^41 + 81 * q^42 + 418 * q^43 - 70 * q^44 + 252 * q^45 - 526 * q^46 + 580 * q^47 - 547 * q^48 + 997 * q^49 - 938 * q^50 + 580 * q^51 - 998 * q^52 + 1512 * q^53 - 73 * q^54 + 200 * q^55 - 1040 * q^56 + 700 * q^57 - 338 * q^58 - 300 * q^59 + 429 * q^60 - 314 * q^61 + 24 * q^62 + 388 * q^63 + 38 * q^64 - 8 * q^65 - 115 * q^66 - 298 * q^67 - 40 * q^68 - 84 * q^69 + 938 * q^70 + 400 * q^71 - 843 * q^72 + 422 * q^73 + 1248 * q^74 - 695 * q^75 + 1506 * q^76 + 170 * q^77 - 293 * q^78 - 322 * q^79 + 1572 * q^80 - 1371 * q^81 + 794 * q^82 - 420 * q^83 - 383 * q^84 - 1560 * q^85 - 8 * q^86 - 1100 * q^87 - 260 * q^88 - 436 * q^89 - 1027 * q^90 - 2504 * q^91 - 2308 * q^92 - 1936 * q^93 - 3630 * q^94 - 1500 * q^95 - 2951 * q^96 - 2274 * q^97 - 4842 * q^98 - 460 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1452))\)

We only show spaces with odd 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
1452.3.d	\(\chi_{1452}(1451, \cdot)\)	n/a	416	1
1452.3.e	\(\chi_{1452}(485, \cdot)\)	1452.3.e.a	1	1
		1452.3.e.b	1
		1452.3.e.c	1
		1452.3.e.d	2
		1452.3.e.e	2
		1452.3.e.f	2
		1452.3.e.g	4
		1452.3.e.h	4
		1452.3.e.i	6
		1452.3.e.j	6
		1452.3.e.k	12
		1452.3.e.l	16
		1452.3.e.m	16
1452.3.f	\(\chi_{1452}(241, \cdot)\)	1452.3.f.a	4	1
		1452.3.f.b	8
		1452.3.f.c	8
		1452.3.f.d	16
1452.3.g	\(\chi_{1452}(727, \cdot)\)	n/a	218	1
1452.3.k	\(\chi_{1452}(487, \cdot)\)	n/a	864	4
1452.3.l	\(\chi_{1452}(457, \cdot)\)	n/a	144	4
1452.3.m	\(\chi_{1452}(245, \cdot)\)	n/a	288	4
1452.3.n	\(\chi_{1452}(215, \cdot)\)	n/a	1664	4
1452.3.s	\(\chi_{1452}(67, \cdot)\)	n/a	2640	10
1452.3.t	\(\chi_{1452}(109, \cdot)\)	n/a	440	10
1452.3.u	\(\chi_{1452}(89, \cdot)\)	n/a	880	10
1452.3.v	\(\chi_{1452}(131, \cdot)\)	n/a	5240	10
1452.3.bb	\(\chi_{1452}(35, \cdot)\)	n/a	20960	40
1452.3.bc	\(\chi_{1452}(5, \cdot)\)	n/a	3520	40
1452.3.bd	\(\chi_{1452}(13, \cdot)\)	n/a	1760	40
1452.3.be	\(\chi_{1452}(31, \cdot)\)	n/a	10560	40

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1452))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1452)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 2}\)