Space of modular forms of level 3751, weight 1, and Character 3751.t

• Label: 3751.1.t
• Level: $3751$
• Weight: $1$
• Character orbit: 3751.t
• Rep. character: $\chi_{3751}(2138,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $68$
• Newform subspaces: $7$
• Sturm bound: $352$
• Trace bound: $8$

Defining parameters

Level:	$N$	$=$	$3751 = 11^{2} \cdot 31$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	3751.t (of order $10$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$341$
Character field:			$\Q(\zeta_{10})$
Newform subspaces:			$7$
Sturm bound:			$352$
Trace bound:			$8$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(3751, [\chi])$.

	Total	New	Old
Modular forms	116	100	16
Cusp forms	68	68	0
Eisenstein series	48	32	16

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	68	0	0	0

Trace form

68 * q - 15 * q^4 + 2 * q^5 - 17 * q^9 + 4 * q^14 - 13 * q^16 + 6 * q^20 - 15 * q^25 + q^31 - 15 * q^36 + 4 * q^38 - 8 * q^45 + 2 * q^47 - 15 * q^49 - 32 * q^56 + 2 * q^59 - 11 * q^64 - 8 * q^67 + 8 * q^70 + 2 * q^71 + 10 * q^80 - 17 * q^81 + 4 * q^82 + 2 * q^97

Decomposition of $S_{1}^{\mathrm{new}}(3751, [\chi])$ 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3751.1.t.a	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31})$	None					31.1.b.a	$8$	$0$	$-1$	$0$	$1$	$-1$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
3751.1.t.b	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{2}$	$\Q(\sqrt{-11})$, $\Q(\sqrt{-31})$	$\Q(\sqrt{341})$		✓			3751.1.d.a	$16$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{10}q^{4}+\zeta_{10}^{2}q^{5}-\zeta_{10}^{3}q^{9}+\zeta_{10}^{2}q^{16}+\cdots$
3751.1.t.c	$3751$	$1$	3751.t	341.t	$10$	$4$	$1$	$1.872$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-31})$	None					31.1.b.a	$8$	$0$	$1$	$0$	$1$	$1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}^{2}q^{5}+\zeta_{10}q^{7}+\zeta_{10}^{4}q^{8}+\cdots$
3751.1.t.d	$3751$	$1$	3751.t	341.t	$10$	$8$	$2$	$1.872$	8.0.324000000.3	$D_{6}$	$\Q(\sqrt{-31})$	None		✓			3751.1.d.c	$16$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\beta _{7}q^{2}+2\beta _{4}q^{4}+(1+\beta _{2}+\beta _{4}+\beta _{6}+\cdots)q^{5}+\cdots$
3751.1.t.e	$3751$	$1$	3751.t	341.t	$10$	$12$	$3$	$1.872$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-31})$	None		✓			3751.1.d.d	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
3751.1.t.f	$3751$	$1$	3751.t	341.t	$10$	$12$	$3$	$1.872$	12.0.$\cdots$.1	$D_{9}$	$\Q(\sqrt{-31})$	None		✓			3751.1.d.d	$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{5}q^{2}+(\beta _{6}+\beta _{7}-\beta _{8})q^{4}+(\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
3751.1.t.g	$3751$	$1$	3751.t	341.t	$10$	$24$	$6$	$1.872$	24.0.$\cdots$.2	$D_{18}$	$\Q(\sqrt{-31})$	None		✓	✓		3751.1.d.f	$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\beta _{1}-\beta _{9}+\beta _{11}-\beta _{14}+\beta _{17}+\cdots)q^{2}+\cdots$