Space of modular forms of level 1425, weight 1, and Character 1425.t

• Label: 1425.1.t
• Level: $1425$
• Weight: $1$
• Character orbit: 1425.t
• Rep. character: $\chi_{1425}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $200$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$1425 = 3 \cdot 5^{2} \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1425.t (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$57$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$2$
Sturm bound:			$200$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(1425, [\chi])$.

	Total	New	Old
Modular forms	36	18	18
Cusp forms	12	6	6
Eisenstein series	24	12	12

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	6	0	0	0

Trace form

6 * q + q^3 - q^4 + 2 * q^6 + 2 * q^7 + q^9 - 2 * q^12 - q^13 + q^16 + 4 * q^19 + q^21 + 2 * q^24 - 2 * q^27 - q^28 - 6 * q^31 + 2 * q^34 - q^36 + 2 * q^37 - 2 * q^39 - q^43 - 8 * q^46 + q^48 - 4 * q^49 + 2 * q^51 - q^52 - 2 * q^54 + q^57 - 3 * q^61 - q^63 - 2 * q^64 - q^67 - 8 * q^69 - q^73 - q^76 + 5 * q^79 - 3 * q^81 - 2 * q^84 - q^91 - q^93 - 4 * q^94 + 2 * q^97

Decomposition of $S_{1}^{\mathrm{new}}(1425, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1425.1.t.a	$1425$	$1$	1425.t	57.h	$6$	$2$	$1$	$0.711$	$\Q(\sqrt{-3})$	$D_{3}$	$\Q(\sqrt{-3})$	None					57.1.h.a	$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{7}-\zeta_{6}q^{9}-q^{12}+\cdots$
1425.1.t.b	$1425$	$1$	1425.t	57.h	$6$	$4$	$2$	$0.711$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-15})$	None			✓		285.1.n.a	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{4}q^{6}+\cdots$

Decomposition of $S_{1}^{\mathrm{old}}(1425, [\chi])$ into lower level spaces

$S_{1}^{\mathrm{old}}(1425, [\chi]) \simeq$ $S_{1}^{\mathrm{new}}(57, [\chi])$$^{\oplus 3}$