Space of modular forms of level 3064 and weight 2

• Label: 3064.2
• Level: 3064
• Weight: 2
• Dimension: 164260
• Nonzero newspaces: 6
• Sturm bound: 1173504
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 3064 = 2^{3} \cdot 383 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(1173504\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3064))\).

	Total	New	Old
Modular forms	295668	165784	129884
Cusp forms	291085	164260	126825
Eisenstein series	4583	1524	3059

Trace form

164260 * q - 382 * q^2 - 382 * q^3 - 382 * q^4 - 382 * q^6 - 382 * q^7 - 382 * q^8 - 764 * q^9 - 382 * q^10 - 382 * q^11 - 382 * q^12 - 382 * q^14 - 382 * q^15 - 382 * q^16 - 764 * q^17 - 382 * q^18 - 382 * q^19 - 382 * q^20 - 382 * q^22 - 382 * q^23 - 382 * q^24 - 764 * q^25 - 382 * q^26 - 382 * q^27 - 382 * q^28 - 382 * q^30 - 382 * q^31 - 382 * q^32 - 764 * q^33 - 382 * q^34 - 382 * q^35 - 382 * q^36 - 382 * q^38 - 382 * q^39 - 382 * q^40 - 764 * q^41 - 382 * q^42 - 382 * q^43 - 382 * q^44 - 382 * q^46 - 382 * q^47 - 382 * q^48 - 764 * q^49 - 382 * q^50 - 382 * q^51 - 382 * q^52 - 382 * q^54 - 382 * q^55 - 382 * q^56 - 764 * q^57 - 382 * q^58 - 382 * q^59 - 382 * q^60 - 382 * q^62 - 382 * q^63 - 382 * q^64 - 764 * q^65 - 382 * q^66 - 382 * q^67 - 382 * q^68 - 382 * q^70 - 382 * q^71 - 382 * q^72 - 764 * q^73 - 382 * q^74 - 382 * q^75 - 382 * q^76 - 382 * q^78 - 382 * q^79 - 382 * q^80 - 764 * q^81 - 382 * q^82 - 382 * q^83 - 382 * q^84 - 382 * q^86 - 382 * q^87 - 382 * q^88 - 764 * q^89 - 382 * q^90 - 382 * q^91 - 382 * q^92 - 382 * q^94 - 382 * q^95 - 382 * q^96 - 764 * q^97 - 382 * q^98 - 382 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3064))\)

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
3064.2.a	\(\chi_{3064}(1, \cdot)\)	3064.2.a.a	2	1
		3064.2.a.b	3
		3064.2.a.c	19
		3064.2.a.d	21
		3064.2.a.e	24
		3064.2.a.f	27
3064.2.b	\(\chi_{3064}(3063, \cdot)\)	None	0	1
3064.2.c	\(\chi_{3064}(1533, \cdot)\)	n/a	382	1
3064.2.h	\(\chi_{3064}(1531, \cdot)\)	n/a	382	1
3064.2.i	\(\chi_{3064}(9, \cdot)\)	n/a	18240	190
3064.2.j	\(\chi_{3064}(11, \cdot)\)	n/a	72580	190
3064.2.o	\(\chi_{3064}(21, \cdot)\)	n/a	72580	190
3064.2.p	\(\chi_{3064}(15, \cdot)\)	None	0	190

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3064)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(383))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(766))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1532))\)\(^{\oplus 2}\)