LMFDB - Space of Modular Forms of Level 134, Weight 2, and Character 134.c

Defining parameters

Level:	$ N $	=	$ 134 = 2 \cdot 67 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	134.c (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	=	$ 67 $
Character field:			$\Q(\zeta_{3})$
Newforms:			$ 3 $
Sturm bound:			$34$
Trace bound:			$2$
Distinguishing $T_p$:			$3$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(134, [\chi])$.

	Total	New	Old
Modular forms	38	10	28
Cusp forms	30	10	20
Eisenstein series	8	0	8

Trace form

$10q $ $\mathstrut -\mathstrut q^{2} $ $\mathstrut +\mathstrut 6q^{3} $ $\mathstrut -\mathstrut 5q^{4} $ $\mathstrut +\mathstrut 3q^{6} $ $\mathstrut +\mathstrut 2q^{7} $ $\mathstrut +\mathstrut 2q^{8} $ $\mathstrut +\mathstrut 8q^{9} $ $\mathstrut -\mathstrut 2q^{11} $ $\mathstrut -\mathstrut 3q^{12} $ $\mathstrut -\mathstrut 6q^{13} $ $\mathstrut -\mathstrut 8q^{14} $ $\mathstrut -\mathstrut 16q^{15} $ $\mathstrut -\mathstrut 5q^{16} $ $\mathstrut +\mathstrut 3q^{17} $ $\mathstrut -\mathstrut 2q^{18} $ $\mathstrut -\mathstrut q^{19} $ $\mathstrut +\mathstrut 2q^{21} $ $\mathstrut +\mathstrut 20q^{22} $ $\mathstrut -\mathstrut 10q^{23} $ $\mathstrut -\mathstrut 6q^{24} $ $\mathstrut -\mathstrut 18q^{25} $ $\mathstrut +\mathstrut 30q^{27} $ $\mathstrut +\mathstrut 2q^{28} $ $\mathstrut -\mathstrut 6q^{29} $ $\mathstrut -\mathstrut 2q^{30} $ $\mathstrut -\mathstrut 14q^{31} $ $\mathstrut -\mathstrut q^{32} $ $\mathstrut +\mathstrut 2q^{33} $ $\mathstrut +\mathstrut 3q^{34} $ $\mathstrut +\mathstrut 14q^{35} $ $\mathstrut -\mathstrut 4q^{36} $ $\mathstrut +\mathstrut 16q^{37} $ $\mathstrut -\mathstrut 5q^{38} $ $\mathstrut -\mathstrut 24q^{39} $ $\mathstrut -\mathstrut 2q^{41} $ $\mathstrut -\mathstrut 20q^{42} $ $\mathstrut -\mathstrut 14q^{43} $ $\mathstrut -\mathstrut 2q^{44} $ $\mathstrut -\mathstrut 48q^{45} $ $\mathstrut +\mathstrut 10q^{46} $ $\mathstrut -\mathstrut 4q^{47} $ $\mathstrut -\mathstrut 3q^{48} $ $\mathstrut +\mathstrut 5q^{49} $ $\mathstrut +\mathstrut 9q^{50} $ $\mathstrut +\mathstrut 13q^{51} $ $\mathstrut +\mathstrut 12q^{52} $ $\mathstrut +\mathstrut 36q^{53} $ $\mathstrut -\mathstrut 15q^{54} $ $\mathstrut +\mathstrut 8q^{55} $ $\mathstrut +\mathstrut 4q^{56} $ $\mathstrut -\mathstrut 3q^{57} $ $\mathstrut +\mathstrut 12q^{58} $ $\mathstrut -\mathstrut 6q^{59} $ $\mathstrut +\mathstrut 8q^{60} $ $\mathstrut +\mathstrut 8q^{61} $ $\mathstrut +\mathstrut 8q^{62} $ $\mathstrut -\mathstrut 8q^{63} $ $\mathstrut +\mathstrut 10q^{64} $ $\mathstrut +\mathstrut 18q^{65} $ $\mathstrut +\mathstrut 40q^{66} $ $\mathstrut +\mathstrut 34q^{67} $ $\mathstrut -\mathstrut 6q^{68} $ $\mathstrut +\mathstrut 2q^{69} $ $\mathstrut -\mathstrut 8q^{70} $ $\mathstrut -\mathstrut 14q^{71} $ $\mathstrut +\mathstrut 4q^{72} $ $\mathstrut +\mathstrut 25q^{73} $ $\mathstrut -\mathstrut 10q^{74} $ $\mathstrut -\mathstrut 6q^{75} $ $\mathstrut +\mathstrut 2q^{76} $ $\mathstrut -\mathstrut 14q^{77} $ $\mathstrut +\mathstrut 22q^{79} $ $\mathstrut -\mathstrut 14q^{81} $ $\mathstrut +\mathstrut 20q^{82} $ $\mathstrut -\mathstrut 56q^{83} $ $\mathstrut +\mathstrut 2q^{84} $ $\mathstrut +\mathstrut 16q^{85} $ $\mathstrut -\mathstrut 7q^{86} $ $\mathstrut -\mathstrut 6q^{87} $ $\mathstrut -\mathstrut 10q^{88} $ $\mathstrut +\mathstrut 26q^{89} $ $\mathstrut -\mathstrut 6q^{90} $ $\mathstrut +\mathstrut 20q^{92} $ $\mathstrut -\mathstrut 26q^{93} $ $\mathstrut +\mathstrut 40q^{94} $ $\mathstrut -\mathstrut 30q^{95} $ $\mathstrut +\mathstrut 3q^{96} $ $\mathstrut +\mathstrut 25q^{97} $ $\mathstrut -\mathstrut 17q^{98} $ $\mathstrut -\mathstrut 16q^{99} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(134, [\chi])$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
134.2.c.a	$2$	$1.070$	$\Q(\sqrt{-3}) $	None	$-1$	$-2$	$4$	$4$	$q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+2q^{5}+\cdots$
134.2.c.b	$4$	$1.070$	$\Q(\sqrt{-3}, \sqrt{-7})$	None	$-2$	$2$	$-4$	$-1$	$q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1})q^{4}+\cdots$
134.2.c.c	$4$	$1.070$	$\Q(\sqrt{-3}, \sqrt{5})$	None	$2$	$6$	$0$	$-1$	$q+(1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(134, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(134, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(67, [\chi])$$^{\oplus 2}$

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 134 = 2 \cdot 67 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	134.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	=	\( 67 \)
Character field:			\(\Q(\zeta_{3})\)
Newforms:			\( 3 \)
Sturm bound:			\(34\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
134.2.c.a	\(2\)	\(1.070\)	\(\Q(\sqrt{-3}) \)	None	\(-1\)	\(-2\)	\(4\)	\(4\)	\(q+(-1+\zeta_{6})q^{2}-q^{3}-\zeta_{6}q^{4}+2q^{5}+\cdots\)
134.2.c.b	\(4\)	\(1.070\)	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None	\(-2\)	\(2\)	\(-4\)	\(-1\)	\(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-1-\beta _{1})q^{4}+\cdots\)
134.2.c.c	\(4\)	\(1.070\)	\(\Q(\sqrt{-3}, \sqrt{5})\)	None	\(2\)	\(6\)	\(0\)	\(-1\)	\(q+(1+\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(134, [\chi])\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(134, [\chi])\) into lower level spaces

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	134.2.c

Level	134
Weight	2
Character orbit	c
Rep. character	\(\chi_{134}(29,\cdot)\)
Character field	\(\Q(\zeta_{3})\)
Dimension	10
Newforms	3
Sturm bound	34
Trace bound	2