Space of modular forms of level 3364 and weight 1

• Label: 3364.1
• Level: 3364
• Weight: 1
• Dimension: 300
• Nonzero newspaces: 6
• Newform subspaces: 17
• Sturm bound: 706440
• Trace bound: 1

Defining parameters

Level:	$N$	=	$3364 = 2^{2} \cdot 29^{2}$
Weight:	$k$	=	$1$
Nonzero newspaces:			$6$
Newform subspaces:			$17$
Sturm bound:			$706440$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(3364))$.

	Total	New	Old
Modular forms	3326	1449	1877
Cusp forms	316	300	16
Eisenstein series	3010	1149	1861

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	300	0	0	0

Trace form

300 * q + q^2 - q^4 + 4 * q^5 + 2 * q^6 + q^8 + q^9 + 2 * q^10 + 4 * q^13 - q^16 + 2 * q^17 + q^18 - 10 * q^20 + 2 * q^22 + 2 * q^24 + 3 * q^25 - 12 * q^26 + 26 * q^30 + q^32 - 2 * q^33 - 12 * q^34 + q^36 + 2 * q^37 - 4 * q^38 - 12 * q^40 + 2 * q^41 - 12 * q^45 - q^49 + 3 * q^50 + 4 * q^52 - 10 * q^53 - 2 * q^54 + 4 * q^57 + 2 * q^61 + 2 * q^62 - q^64 - 12 * q^65 + 2 * q^68 + q^72 - 12 * q^73 + 2 * q^74 - 2 * q^78 + 4 * q^80 + 3 * q^81 + 2 * q^82 + 4 * q^85 + 2 * q^86 - 26 * q^88 + 2 * q^89 + 2 * q^90 - 2 * q^93 + 2 * q^94 + 2 * q^96 - 12 * q^97 + q^98

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(3364))$

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
3364.1.b	$\chi_{3364}(1683, \cdot)$	3364.1.b.a	2	1
		3364.1.b.b	3
		3364.1.b.c	3
3364.1.d	$\chi_{3364}(3363, \cdot)$	3364.1.d.a	6	1
3364.1.f	$\chi_{3364}(41, \cdot)$	None	0	2
3364.1.h	$\chi_{3364}(63, \cdot)$	3364.1.h.a	6	6
		3364.1.h.b	6
		3364.1.h.c	12
		3364.1.h.d	12
		3364.1.h.e	12
3364.1.j	$\chi_{3364}(571, \cdot)$	3364.1.j.a	6	6
		3364.1.j.b	6
		3364.1.j.c	6
		3364.1.j.d	6
		3364.1.j.e	6
		3364.1.j.f	12
3364.1.k	$\chi_{3364}(137, \cdot)$	None	0	12
3364.1.n	$\chi_{3364}(115, \cdot)$	None	0	28
3364.1.p	$\chi_{3364}(59, \cdot)$	3364.1.p.a	28	28
3364.1.q	$\chi_{3364}(17, \cdot)$	None	0	56
3364.1.t	$\chi_{3364}(7, \cdot)$	3364.1.t.a	168	168
3364.1.v	$\chi_{3364}(35, \cdot)$	None	0	168
3364.1.x	$\chi_{3364}(21, \cdot)$	None	0	336

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(3364))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(3364)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 9}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(29))$$^{\oplus 6}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(58))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(116))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(841))$$^{\oplus 3}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(1682))$$^{\oplus 2}$