Space of modular forms of level 345 and weight 1

• Label: 345.1
• Level: 345
• Weight: 1
• Dimension: 20
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 8448
• Trace bound: 0

Defining parameters

Level:	$N$	=	$345 = 3 \cdot 5 \cdot 23$
Weight:	$k$	=	$1$
Nonzero newspaces:			$1$
Newform subspaces:			$2$
Sturm bound:			$8448$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(\Gamma_1(345))$.

	Total	New	Old
Modular forms	376	148	228
Cusp forms	24	20	4
Eisenstein series	352	128	224

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	20	0	0	0

Trace form

20 * q - 6 * q^4 - 4 * q^6 - 2 * q^9 - 4 * q^10 - 2 * q^15 - 10 * q^16 - 4 * q^19 - 8 * q^24 - 2 * q^25 - 4 * q^31 + 14 * q^34 - 6 * q^36 + 14 * q^40 - 4 * q^46 - 2 * q^49 - 4 * q^51 + 18 * q^54 + 16 * q^60 - 4 * q^61 + 8 * q^64 - 2 * q^69 + 10 * q^76 - 4 * q^79 - 2 * q^81 - 4 * q^85 - 4 * q^90 - 8 * q^94 + 10 * q^96

Decomposition of $S_{1}^{\mathrm{new}}(\Gamma_1(345))$

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
345.1.d	$\chi_{345}(229, \cdot)$	None	0	1
345.1.e	$\chi_{345}(116, \cdot)$	None	0	1
345.1.f	$\chi_{345}(254, \cdot)$	None	0	1
345.1.g	$\chi_{345}(91, \cdot)$	None	0	1
345.1.k	$\chi_{345}(208, \cdot)$	None	0	2
345.1.l	$\chi_{345}(68, \cdot)$	None	0	2
345.1.o	$\chi_{345}(61, \cdot)$	None	0	10
345.1.p	$\chi_{345}(29, \cdot)$	345.1.p.a	10	10
		345.1.p.b	10
345.1.q	$\chi_{345}(26, \cdot)$	None	0	10
345.1.r	$\chi_{345}(19, \cdot)$	None	0	10
345.1.u	$\chi_{345}(17, \cdot)$	None	0	20
345.1.v	$\chi_{345}(13, \cdot)$	None	0	20

Decomposition of $S_{1}^{\mathrm{old}}(\Gamma_1(345))$ into lower level spaces

$S_{1}^{\mathrm{old}}(\Gamma_1(345)) \cong$ $S_{1}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 8}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(3))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(15))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(23))$$^{\oplus 4}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(69))$$^{\oplus 2}$$\oplus$$S_{1}^{\mathrm{new}}(\Gamma_1(115))$$^{\oplus 2}$