Space of modular forms of level 1449 and weight 2

• Label: 1449.2
• Level: 1449
• Weight: 2
• Dimension: 56520
• Nonzero newspaces: 40
• Sturm bound: 304128
• Trace bound: 22

Defining parameters

Level:	\( N \)	=	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(304128\)
Trace bound:			\(22\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1449))\).

	Total	New	Old
Modular forms	78144	58412	19732
Cusp forms	73921	56520	17401
Eisenstein series	4223	1892	2331

Trace form

56520 * q - 114 * q^2 - 152 * q^3 - 106 * q^4 - 108 * q^5 - 152 * q^6 - 139 * q^7 - 276 * q^8 - 152 * q^9 - 312 * q^10 - 96 * q^11 - 176 * q^12 - 100 * q^13 - 159 * q^14 - 416 * q^15 - 94 * q^16 - 134 * q^17 - 200 * q^18 - 342 * q^19 - 116 * q^20 - 232 * q^21 - 264 * q^22 - 94 * q^23 - 400 * q^24 - 70 * q^25 - 136 * q^26 - 188 * q^27 - 385 * q^28 - 272 * q^29 - 236 * q^30 - 90 * q^31 - 166 * q^32 - 200 * q^33 - 112 * q^34 - 191 * q^35 - 512 * q^36 - 280 * q^37 - 130 * q^38 - 224 * q^39 - 52 * q^40 - 208 * q^41 - 328 * q^42 - 226 * q^43 - 242 * q^44 - 248 * q^45 - 244 * q^46 - 212 * q^47 - 128 * q^48 - 105 * q^49 - 158 * q^50 - 152 * q^51 + 72 * q^52 - 4 * q^53 - 180 * q^54 - 344 * q^55 - 134 * q^56 - 428 * q^57 - 214 * q^58 - 160 * q^59 - 388 * q^60 - 352 * q^61 - 216 * q^62 - 138 * q^63 - 1264 * q^64 - 450 * q^65 - 420 * q^66 - 240 * q^67 - 750 * q^68 - 360 * q^69 - 642 * q^70 - 636 * q^71 - 572 * q^72 - 556 * q^73 - 662 * q^74 - 484 * q^75 - 626 * q^76 - 358 * q^77 - 728 * q^78 - 380 * q^79 - 666 * q^80 - 496 * q^81 - 564 * q^82 - 374 * q^83 - 616 * q^84 - 290 * q^85 - 296 * q^86 - 332 * q^87 - 24 * q^88 - 264 * q^89 - 564 * q^90 - 472 * q^91 - 264 * q^92 - 556 * q^93 - 70 * q^94 - 162 * q^95 - 688 * q^96 - 46 * q^97 - 356 * q^98 - 584 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1449))\)

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
1449.2.a	\(\chi_{1449}(1, \cdot)\)	1449.2.a.a	1	1
		1449.2.a.b	1
		1449.2.a.c	1
		1449.2.a.d	1
		1449.2.a.e	1
		1449.2.a.f	2
		1449.2.a.g	2
		1449.2.a.h	2
		1449.2.a.i	2
		1449.2.a.j	2
		1449.2.a.k	2
		1449.2.a.l	3
		1449.2.a.m	3
		1449.2.a.n	4
		1449.2.a.o	4
		1449.2.a.p	4
		1449.2.a.q	4
		1449.2.a.r	5
		1449.2.a.s	5
		1449.2.a.t	5
1449.2.d	\(\chi_{1449}(944, \cdot)\)	1449.2.d.a	56	1
1449.2.e	\(\chi_{1449}(827, \cdot)\)	1449.2.e.a	48	1
1449.2.h	\(\chi_{1449}(1126, \cdot)\)	1449.2.h.a	2	1
		1449.2.h.b	4
		1449.2.h.c	4
		1449.2.h.d	8
		1449.2.h.e	12
		1449.2.h.f	12
		1449.2.h.g	12
		1449.2.h.h	12
		1449.2.h.i	12
1449.2.i	\(\chi_{1449}(415, \cdot)\)	n/a	148	2
1449.2.j	\(\chi_{1449}(484, \cdot)\)	n/a	264	2
1449.2.k	\(\chi_{1449}(760, \cdot)\)	n/a	352	2
1449.2.l	\(\chi_{1449}(277, \cdot)\)	n/a	352	2
1449.2.m	\(\chi_{1449}(137, \cdot)\)	n/a	376	2
1449.2.n	\(\chi_{1449}(668, \cdot)\)	n/a	352	2
1449.2.s	\(\chi_{1449}(712, \cdot)\)	n/a	156	2
1449.2.t	\(\chi_{1449}(160, \cdot)\)	n/a	376	2
1449.2.y	\(\chi_{1449}(850, \cdot)\)	n/a	376	2
1449.2.bb	\(\chi_{1449}(344, \cdot)\)	n/a	288	2
1449.2.bc	\(\chi_{1449}(461, \cdot)\)	n/a	352	2
1449.2.bd	\(\chi_{1449}(620, \cdot)\)	n/a	128	2
1449.2.be	\(\chi_{1449}(530, \cdot)\)	n/a	120	2
1449.2.bj	\(\chi_{1449}(47, \cdot)\)	n/a	352	2
1449.2.bk	\(\chi_{1449}(758, \cdot)\)	n/a	376	2
1449.2.bl	\(\chi_{1449}(229, \cdot)\)	n/a	376	2
1449.2.bo	\(\chi_{1449}(64, \cdot)\)	n/a	600	10
1449.2.bp	\(\chi_{1449}(181, \cdot)\)	n/a	780	10
1449.2.bs	\(\chi_{1449}(134, \cdot)\)	n/a	480	10
1449.2.bt	\(\chi_{1449}(62, \cdot)\)	n/a	640	10
1449.2.bw	\(\chi_{1449}(25, \cdot)\)	n/a	3760	20
1449.2.bx	\(\chi_{1449}(4, \cdot)\)	n/a	3760	20
1449.2.by	\(\chi_{1449}(85, \cdot)\)	n/a	2880	20
1449.2.bz	\(\chi_{1449}(100, \cdot)\)	n/a	1560	20
1449.2.cc	\(\chi_{1449}(40, \cdot)\)	n/a	3760	20
1449.2.cd	\(\chi_{1449}(65, \cdot)\)	n/a	3760	20
1449.2.ce	\(\chi_{1449}(59, \cdot)\)	n/a	3760	20
1449.2.cj	\(\chi_{1449}(26, \cdot)\)	n/a	1280	20
1449.2.ck	\(\chi_{1449}(44, \cdot)\)	n/a	1280	20
1449.2.cl	\(\chi_{1449}(41, \cdot)\)	n/a	3760	20
1449.2.cm	\(\chi_{1449}(113, \cdot)\)	n/a	2880	20
1449.2.cp	\(\chi_{1449}(61, \cdot)\)	n/a	3760	20
1449.2.cu	\(\chi_{1449}(34, \cdot)\)	n/a	3760	20
1449.2.cv	\(\chi_{1449}(10, \cdot)\)	n/a	1560	20
1449.2.da	\(\chi_{1449}(101, \cdot)\)	n/a	3760	20
1449.2.db	\(\chi_{1449}(11, \cdot)\)	n/a	3760	20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1449))\) into lower level spaces

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