Space of modular forms of level 9027 and weight 2

• Label: 9027.2
• Level: 9027
• Weight: 2
• Dimension: 2354736
• Nonzero newspaces: 40
• Sturm bound: 12026880

Defining parameters

Level:	\( N \)	=	\( 9027 = 3^{2} \cdot 17 \cdot 59 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(12026880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9027))\).

	Total	New	Old
Modular forms	3021568	2370128	651440
Cusp forms	2991873	2354736	637137
Eisenstein series	29695	15392	14303

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9027))\)

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
9027.2.a	\(\chi_{9027}(1, \cdot)\)	9027.2.a.a	1	1
		9027.2.a.b	1
		9027.2.a.c	1
		9027.2.a.d	1
		9027.2.a.e	1
		9027.2.a.f	2
		9027.2.a.g	2
		9027.2.a.h	3
		9027.2.a.i	4
		9027.2.a.j	10
		9027.2.a.k	14
		9027.2.a.l	14
		9027.2.a.m	16
		9027.2.a.n	16
		9027.2.a.o	17
		9027.2.a.p	18
		9027.2.a.q	18
		9027.2.a.r	21
		9027.2.a.s	22
		9027.2.a.t	24
		9027.2.a.u	26
		9027.2.a.v	35
		9027.2.a.w	35
		9027.2.a.x	43
		9027.2.a.y	43
9027.2.f	\(\chi_{9027}(4249, \cdot)\)	n/a	436	1
9027.2.g	\(\chi_{9027}(4778, \cdot)\)	n/a	320	1
9027.2.h	\(\chi_{9027}(9026, \cdot)\)	n/a	360	1
9027.2.i	\(\chi_{9027}(3010, \cdot)\)	n/a	1856	2
9027.2.j	\(\chi_{9027}(6371, \cdot)\)	n/a	720	2
9027.2.k	\(\chi_{9027}(1594, \cdot)\)	n/a	872	2
9027.2.n	\(\chi_{9027}(3008, \cdot)\)	n/a	2152	2
9027.2.o	\(\chi_{9027}(1769, \cdot)\)	n/a	1920	2
9027.2.p	\(\chi_{9027}(1240, \cdot)\)	n/a	2088	2
9027.2.v	\(\chi_{9027}(1063, \cdot)\)	n/a	1736	4
9027.2.w	\(\chi_{9027}(2123, \cdot)\)	n/a	1440	4
9027.2.ba	\(\chi_{9027}(4603, \cdot)\)	n/a	4176	4
9027.2.bb	\(\chi_{9027}(353, \cdot)\)	n/a	4304	4
9027.2.bd	\(\chi_{9027}(296, \cdot)\)	n/a	2784	8
9027.2.bf	\(\chi_{9027}(235, \cdot)\)	n/a	3584	8
9027.2.bg	\(\chi_{9027}(1946, \cdot)\)	n/a	8608	8
9027.2.bj	\(\chi_{9027}(178, \cdot)\)	n/a	8352	8
9027.2.bk	\(\chi_{9027}(154, \cdot)\)	n/a	11200	28
9027.2.bl	\(\chi_{9027}(473, \cdot)\)	n/a	16704	16
9027.2.bn	\(\chi_{9027}(58, \cdot)\)	n/a	17216	16
9027.2.bp	\(\chi_{9027}(152, \cdot)\)	n/a	10080	28
9027.2.bq	\(\chi_{9027}(188, \cdot)\)	n/a	8960	28
9027.2.br	\(\chi_{9027}(271, \cdot)\)	n/a	12544	28
9027.2.bw	\(\chi_{9027}(205, \cdot)\)	n/a	53760	56
9027.2.bz	\(\chi_{9027}(64, \cdot)\)	n/a	25088	56
9027.2.ca	\(\chi_{9027}(89, \cdot)\)	n/a	20160	56
9027.2.cf	\(\chi_{9027}(16, \cdot)\)	n/a	60256	56
9027.2.cg	\(\chi_{9027}(290, \cdot)\)	n/a	53760	56
9027.2.ch	\(\chi_{9027}(50, \cdot)\)	n/a	60256	56
9027.2.cj	\(\chi_{9027}(8, \cdot)\)	n/a	40320	112
9027.2.ck	\(\chi_{9027}(19, \cdot)\)	n/a	50176	112
9027.2.cm	\(\chi_{9027}(38, \cdot)\)	n/a	120512	112
9027.2.cn	\(\chi_{9027}(4, \cdot)\)	n/a	120512	112
9027.2.cq	\(\chi_{9027}(10, \cdot)\)	n/a	100352	224
9027.2.cs	\(\chi_{9027}(62, \cdot)\)	n/a	80640	224
9027.2.cu	\(\chi_{9027}(25, \cdot)\)	n/a	241024	224
9027.2.cx	\(\chi_{9027}(2, \cdot)\)	n/a	241024	224
9027.2.cz	\(\chi_{9027}(31, \cdot)\)	n/a	482048	448
9027.2.db	\(\chi_{9027}(5, \cdot)\)	n/a	482048	448

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(531))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3009))\)\(^{\oplus 2}\)