Space of modular forms of level 3060, weight 2, and Character 3060.be

• Label: 3060.2.be
• Level: $3060$
• Weight: $2$
• Character orbit: 3060.be
• Rep. character: $\chi_{3060}(361,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $4$
• Sturm bound: $1296$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$3060 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3060.be (of order $4$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$17$
Character field:			$\Q(i)$
Newform subspaces:			$4$
Sturm bound:			$1296$
Trace bound:			$7$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(3060, [\chi])$.

	Total	New	Old
Modular forms	1344	60	1284
Cusp forms	1248	60	1188
Eisenstein series	96	0	96

Trace form

60 * q + 4 * q^11 + 16 * q^13 - 4 * q^17 - 12 * q^23 + 12 * q^29 - 8 * q^31 + 8 * q^35 + 28 * q^37 - 8 * q^41 - 8 * q^47 - 16 * q^55 - 8 * q^61 - 4 * q^65 - 32 * q^67 - 20 * q^71 + 16 * q^73 - 56 * q^79 - 4 * q^85 + 40 * q^89 + 44 * q^91 - 8 * q^95 - 28 * q^97

Decomposition of $S_{2}^{\mathrm{new}}(3060, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3060.2.be.a	$3060$	$2$	3060.be	17.c	$4$	$12$	$6$	$24.434$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					1020.2.bd.a	$2$	$0$	$0$	$0$	$0$	$-4$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{2}q^{5}-\beta _{9}q^{7}+(-2\beta _{1}-\beta _{7}-\beta _{10}+\cdots)q^{11}+\cdots$
3060.2.be.b	$3060$	$2$	3060.be	17.c	$4$	$12$	$6$	$24.434$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					340.2.o.a	$2$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{3}q^{5}+(\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots$
3060.2.be.c	$3060$	$2$	3060.be	17.c	$4$	$12$	$6$	$24.434$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None					1020.2.bd.b	$2$	$0$	$0$	$0$	$0$	$4$	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{5}-\beta _{9}q^{7}+(-\beta _{4}+\beta _{5}-2\beta _{6}+\cdots)q^{11}+\cdots$
3060.2.be.d	$3060$	$2$	3060.be	17.c	$4$	$24$	$12$	$24.434$		None		✓	✓		3060.2.be.d	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$

Decomposition of $S_{2}^{\mathrm{old}}(3060, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(3060, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(34, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(51, [\chi])$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(68, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(85, [\chi])$$^{\oplus 9}$$\oplus$$S_{2}^{\mathrm{new}}(102, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(153, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(170, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(204, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(255, [\chi])$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(306, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(340, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(510, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(612, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(765, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(1020, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(1530, [\chi])$$^{\oplus 2}$