LMFDB - Space of modular forms of level 136, weight 2, and Character 136.n

Defining parameters

The following table gives the dimensions of various subspaces of $M_{2}(136, [\chi])$.

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
136.2.n.a	$4$	$1.086$	$\Q(\zeta_{8})$	None	$0$	$-4$	$4$	$-4$	$q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots$
136.2.n.b	$4$	$1.086$	$\Q(\zeta_{8})$	None	$0$	$4$	$-8$	$4$	$q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots$
136.2.n.c	$12$	$1.086$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	$0$	$0$	$4$	$0$	$q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots$

$ S_{2}^{\mathrm{old}}(136, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(17, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(34, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(68, [\chi])$$^{\oplus 2}$

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Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	$q$-expansion
136.2.n.a	$4$	$1.086$	\(\Q(\zeta_{8})\)	None	\(0\)	\(-4\)	\(4\)	\(-4\)	\(q+(-1-\zeta_{8})q^{3}+(1-\zeta_{8})q^{5}+(-1+\cdots)q^{7}+\cdots\)
136.2.n.b	$4$	$1.086$	\(\Q(\zeta_{8})\)	None	\(0\)	\(4\)	\(-8\)	\(4\)	\(q+(1+\zeta_{8}-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}+\cdots)q^{5}+\cdots\)
136.2.n.c	$12$	$1.086$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	\(0\)	\(0\)	\(4\)	\(0\)	\(q+\beta _{2}q^{3}+\beta _{8}q^{5}+(1-\beta _{3}-\beta _{6}-\beta _{8}+\cdots)q^{7}+\cdots\)