LMFDB - Space of modular forms of level 153, weight 4, and Character 153.n

Defining parameters

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.n (of order $12$ and degree $4$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 153 $
Character field:			$\Q(\zeta_{12})$
Newform subspaces:			$ 1 $
Sturm bound:			$72$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{4}(153, [\chi])$.

	Total	New
Modular forms	224	224
Cusp forms	208	208
Eisenstein series	16	16

Trace form

$ 208 q - 6 q^{3} + 396 q^{4} - 2 q^{5} - 40 q^{6} - 2 q^{7} - 40 q^{10} - 60 q^{11} + 96 q^{12} - 4 q^{13} - 84 q^{14} - 1444 q^{16} - 8 q^{17} - 152 q^{18} + 270 q^{20} - 184 q^{21} - 70 q^{22} + 82 q^{23}+ \cdots - 2658 q^{99}+O(q^{100}) $

Decomposition of $S_{4}^{\mathrm{new}}(153, [\chi])$ 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
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
153.4.n.a	$153$	$4$	153.n	153.n	$12$	$208$	$52$	$9.027$		None		✓	✓	✓	153.4.n.a	$4$	$0$	$0$	$-6$	$-2$	$-2$		$\mathrm{SU}(2)[C_{12}]$

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Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 153 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{4}^{\mathrm{new}}(153, [\chi])\) into newform subspaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	153.4.n

Level	$153$
Weight	$4$
Character orbit	153.n
Rep. character	$\chi_{153}(4,\cdot)$
Character field	$\Q(\zeta_{12})$
Dimension	$208$
Newform subspaces	$1$
Sturm bound	$72$
Trace bound	$0$