Space of modular forms of level 1449 and weight 4

• Label: 1449.4
• Level: 1449
• Weight: 4
• Dimension: 171452
• Nonzero newspaces: 40
• Sturm bound: 608256
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(608256\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1449))\).

	Total	New	Old
Modular forms	230208	173344	56864
Cusp forms	225984	171452	54532
Eisenstein series	4224	1892	2332

Trace form

171452 * q - 126 * q^2 - 164 * q^3 - 166 * q^4 - 198 * q^5 - 116 * q^6 - 169 * q^7 + 24 * q^8 + 28 * q^9 - 240 * q^10 - 378 * q^11 - 872 * q^12 - 644 * q^13 - 1371 * q^14 - 524 * q^15 + 930 * q^16 + 1274 * q^17 + 1384 * q^18 + 366 * q^19 + 1712 * q^20 + 566 * q^21 + 632 * q^22 - 863 * q^23 - 148 * q^24 - 1254 * q^25 - 3824 * q^26 - 2672 * q^27 - 3009 * q^28 - 2170 * q^29 - 2180 * q^30 - 1722 * q^31 - 2210 * q^32 - 848 * q^33 + 636 * q^34 + 1271 * q^35 + 28 * q^36 + 5014 * q^37 + 10270 * q^38 + 5404 * q^39 + 4536 * q^40 + 4336 * q^41 + 4244 * q^42 - 2186 * q^43 - 142 * q^44 - 68 * q^45 - 7098 * q^46 - 3646 * q^47 + 4828 * q^48 - 4639 * q^49 - 4498 * q^50 + 2548 * q^51 - 8732 * q^52 - 5330 * q^53 - 13344 * q^54 - 12504 * q^55 - 23212 * q^56 - 16796 * q^57 + 6294 * q^58 - 7922 * q^59 - 19276 * q^60 + 7690 * q^61 + 3996 * q^62 - 5226 * q^63 + 20888 * q^64 + 16296 * q^65 + 5196 * q^66 - 722 * q^67 + 28182 * q^68 + 10806 * q^69 - 1062 * q^70 + 20826 * q^71 + 33232 * q^72 - 770 * q^73 + 24482 * q^74 + 19268 * q^75 + 24350 * q^76 + 21427 * q^77 + 15832 * q^78 + 10086 * q^79 + 1974 * q^80 - 4972 * q^81 + 8844 * q^82 - 11044 * q^83 - 6280 * q^84 - 18202 * q^85 - 23680 * q^86 + 2188 * q^87 - 24604 * q^88 - 15138 * q^89 - 4356 * q^90 - 14632 * q^91 - 23196 * q^92 - 4540 * q^93 - 31354 * q^94 - 14862 * q^95 - 5632 * q^96 - 11336 * q^97 - 17278 * q^98 - 7172 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1449))\)

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
1449.4.a	\(\chi_{1449}(1, \cdot)\)	1449.4.a.a	1	1
		1449.4.a.b	1
		1449.4.a.c	3
		1449.4.a.d	4
		1449.4.a.e	5
		1449.4.a.f	7
		1449.4.a.g	7
		1449.4.a.h	7
		1449.4.a.i	8
		1449.4.a.j	9
		1449.4.a.k	9
		1449.4.a.l	9
		1449.4.a.m	9
		1449.4.a.n	9
		1449.4.a.o	12
		1449.4.a.p	16
		1449.4.a.q	16
		1449.4.a.r	17
		1449.4.a.s	17
1449.4.d	\(\chi_{1449}(944, \cdot)\)	n/a	176	1
1449.4.e	\(\chi_{1449}(827, \cdot)\)	n/a	144	1
1449.4.h	\(\chi_{1449}(1126, \cdot)\)	n/a	238	1
1449.4.i	\(\chi_{1449}(415, \cdot)\)	n/a	440	2
1449.4.j	\(\chi_{1449}(484, \cdot)\)	n/a	792	2
1449.4.k	\(\chi_{1449}(760, \cdot)\)	n/a	1056	2
1449.4.l	\(\chi_{1449}(277, \cdot)\)	n/a	1056	2
1449.4.m	\(\chi_{1449}(137, \cdot)\)	n/a	1144	2
1449.4.n	\(\chi_{1449}(668, \cdot)\)	n/a	1056	2
1449.4.s	\(\chi_{1449}(712, \cdot)\)	n/a	476	2
1449.4.t	\(\chi_{1449}(160, \cdot)\)	n/a	1144	2
1449.4.y	\(\chi_{1449}(850, \cdot)\)	n/a	1144	2
1449.4.bb	\(\chi_{1449}(344, \cdot)\)	n/a	864	2
1449.4.bc	\(\chi_{1449}(461, \cdot)\)	n/a	1056	2
1449.4.bd	\(\chi_{1449}(620, \cdot)\)	n/a	384	2
1449.4.be	\(\chi_{1449}(530, \cdot)\)	n/a	352	2
1449.4.bj	\(\chi_{1449}(47, \cdot)\)	n/a	1056	2
1449.4.bk	\(\chi_{1449}(758, \cdot)\)	n/a	1144	2
1449.4.bl	\(\chi_{1449}(229, \cdot)\)	n/a	1144	2
1449.4.bo	\(\chi_{1449}(64, \cdot)\)	n/a	1800	10
1449.4.bp	\(\chi_{1449}(181, \cdot)\)	n/a	2380	10
1449.4.bs	\(\chi_{1449}(134, \cdot)\)	n/a	1440	10
1449.4.bt	\(\chi_{1449}(62, \cdot)\)	n/a	1920	10
1449.4.bw	\(\chi_{1449}(25, \cdot)\)	n/a	11440	20
1449.4.bx	\(\chi_{1449}(4, \cdot)\)	n/a	11440	20
1449.4.by	\(\chi_{1449}(85, \cdot)\)	n/a	8640	20
1449.4.bz	\(\chi_{1449}(100, \cdot)\)	n/a	4760	20
1449.4.cc	\(\chi_{1449}(40, \cdot)\)	n/a	11440	20
1449.4.cd	\(\chi_{1449}(65, \cdot)\)	n/a	11440	20
1449.4.ce	\(\chi_{1449}(59, \cdot)\)	n/a	11440	20
1449.4.cj	\(\chi_{1449}(26, \cdot)\)	n/a	3840	20
1449.4.ck	\(\chi_{1449}(44, \cdot)\)	n/a	3840	20
1449.4.cl	\(\chi_{1449}(41, \cdot)\)	n/a	11440	20
1449.4.cm	\(\chi_{1449}(113, \cdot)\)	n/a	8640	20
1449.4.cp	\(\chi_{1449}(61, \cdot)\)	n/a	11440	20
1449.4.cu	\(\chi_{1449}(34, \cdot)\)	n/a	11440	20
1449.4.cv	\(\chi_{1449}(10, \cdot)\)	n/a	4760	20
1449.4.da	\(\chi_{1449}(101, \cdot)\)	n/a	11440	20
1449.4.db	\(\chi_{1449}(11, \cdot)\)	n/a	11440	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1449))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1449)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(483))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1449))\)\(^{\oplus 1}\)