Space of modular forms of level 3332 and weight 1

• Label: 3332.1
• Level: 3332
• Weight: 1
• Dimension: 289
• Nonzero newspaces: 10
• Newform subspaces: 45
• Sturm bound: 677376
• Trace bound: 16

Defining parameters

Level:	\( N \)	=	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 45 \)
Sturm bound:			\(677376\)
Trace bound:			\(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3332))\).

	Total	New	Old
Modular forms	5168	1743	3425
Cusp forms	368	289	79
Eisenstein series	4800	1454	3346

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	289	0	0	0

Trace form

289 * q + q^2 + 5 * q^4 + 2 * q^5 - 5 * q^8 + 5 * q^9 - 2 * q^10 + 2 * q^13 + q^16 + 5 * q^17 - 15 * q^18 - 2 * q^20 + 3 * q^25 - 18 * q^26 - 2 * q^29 + q^32 - 16 * q^33 + q^34 - 31 * q^36 + 2 * q^37 + 2 * q^40 - 2 * q^41 - 2 * q^45 - 33 * q^50 + 2 * q^52 - 18 * q^53 + 2 * q^58 + 2 * q^61 - 13 * q^64 + 8 * q^66 + q^68 + 8 * q^69 - 19 * q^72 - 2 * q^73 - 2 * q^74 - 12 * q^77 + 2 * q^80 + 73 * q^81 - 2 * q^82 - 12 * q^84 - 2 * q^85 + 2 * q^89 - 2 * q^90 - 16 * q^93 + 2 * q^97

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3332))\)

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
3332.1.c	\(\chi_{3332}(2449, \cdot)\)	None	0	1
3332.1.d	\(\chi_{3332}(1667, \cdot)\)	None	0	1
3332.1.g	\(\chi_{3332}(883, \cdot)\)	3332.1.g.a	1	1
		3332.1.g.b	1
		3332.1.g.c	1
		3332.1.g.d	1
		3332.1.g.e	1
		3332.1.g.f	2
		3332.1.g.g	2
		3332.1.g.h	2
		3332.1.g.i	8
3332.1.h	\(\chi_{3332}(1665, \cdot)\)	None	0	1
3332.1.j	\(\chi_{3332}(293, \cdot)\)	None	0	2
3332.1.m	\(\chi_{3332}(2843, \cdot)\)	3332.1.m.a	2	2
		3332.1.m.b	2
		3332.1.m.c	2
3332.1.n	\(\chi_{3332}(509, \cdot)\)	None	0	2
3332.1.o	\(\chi_{3332}(67, \cdot)\)	3332.1.o.a	2	2
		3332.1.o.b	2
		3332.1.o.c	2
		3332.1.o.d	2
		3332.1.o.e	4
		3332.1.o.f	4
		3332.1.o.g	16
3332.1.r	\(\chi_{3332}(851, \cdot)\)	None	0	2
3332.1.s	\(\chi_{3332}(1293, \cdot)\)	None	0	2
3332.1.w	\(\chi_{3332}(491, \cdot)\)	3332.1.w.a	4	4
		3332.1.w.b	4
		3332.1.w.c	4
		3332.1.w.d	4
3332.1.y	\(\chi_{3332}(1273, \cdot)\)	None	0	4
3332.1.z	\(\chi_{3332}(1109, \cdot)\)	None	0	4
3332.1.bc	\(\chi_{3332}(667, \cdot)\)	3332.1.bc.a	4	4
		3332.1.bc.b	4
		3332.1.bc.c	4
		3332.1.bc.d	4
3332.1.bd	\(\chi_{3332}(237, \cdot)\)	None	0	6
3332.1.be	\(\chi_{3332}(407, \cdot)\)	3332.1.be.a	6	6
		3332.1.be.b	6
		3332.1.be.c	12
3332.1.bh	\(\chi_{3332}(239, \cdot)\)	None	0	6
3332.1.bi	\(\chi_{3332}(69, \cdot)\)	None	0	6
3332.1.bk	\(\chi_{3332}(197, \cdot)\)	None	0	8
3332.1.bn	\(\chi_{3332}(979, \cdot)\)	3332.1.bn.a	8	8
		3332.1.bn.b	8
		3332.1.bn.c	8
		3332.1.bn.d	8
3332.1.bp	\(\chi_{3332}(263, \cdot)\)	3332.1.bp.a	8	8
		3332.1.bp.b	8
		3332.1.bp.c	8
		3332.1.bp.d	8
3332.1.br	\(\chi_{3332}(117, \cdot)\)	None	0	8
3332.1.bt	\(\chi_{3332}(183, \cdot)\)	None	0	12
3332.1.bw	\(\chi_{3332}(13, \cdot)\)	None	0	12
3332.1.by	\(\chi_{3332}(341, \cdot)\)	None	0	12
3332.1.bz	\(\chi_{3332}(375, \cdot)\)	None	0	12
3332.1.cc	\(\chi_{3332}(135, \cdot)\)	3332.1.cc.a	12	12
		3332.1.cc.b	12
		3332.1.cc.c	24
3332.1.cd	\(\chi_{3332}(33, \cdot)\)	None	0	12
3332.1.ce	\(\chi_{3332}(31, \cdot)\)	3332.1.ce.a	16	16
		3332.1.ce.b	16
		3332.1.ce.c	16
		3332.1.ce.d	16
3332.1.ch	\(\chi_{3332}(165, \cdot)\)	None	0	16
3332.1.ci	\(\chi_{3332}(321, \cdot)\)	None	0	24
3332.1.ck	\(\chi_{3332}(15, \cdot)\)	None	0	24
3332.1.cm	\(\chi_{3332}(123, \cdot)\)	None	0	24
3332.1.cp	\(\chi_{3332}(89, \cdot)\)	None	0	24
3332.1.cr	\(\chi_{3332}(27, \cdot)\)	None	0	48
3332.1.cs	\(\chi_{3332}(29, \cdot)\)	None	0	48
3332.1.cv	\(\chi_{3332}(145, \cdot)\)	None	0	48
3332.1.cx	\(\chi_{3332}(151, \cdot)\)	None	0	48
3332.1.cz	\(\chi_{3332}(37, \cdot)\)	None	0	96
3332.1.da	\(\chi_{3332}(3, \cdot)\)	None	0	96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3332))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3332)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1666))\)\(^{\oplus 2}\)