LMFDB - Space of modular forms of level 189, weight 2, and Character 189.g

Defining parameters

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.g (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 63 $
Character field:			$\Q(\zeta_{3})$
Newform subspaces:			$ 2 $
Sturm bound:			$48$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(189, [\chi])$.

	Total	New	Old
Modular forms	60	20	40
Cusp forms	36	12	24
Eisenstein series	24	8	16

Trace form

$ 12q - q^{2} - 3q^{4} + 10q^{5} + 12q^{8} + O(q^{10}) $

$ 12q - q^{2} - 3q^{4} + 10q^{5} + 12q^{8} - 6q^{10} - 2q^{11} - 3q^{13} - 11q^{14} + 3q^{16} - 9q^{17} - 4q^{20} - 6q^{22} - 6q^{25} - 16q^{26} - 6q^{28} - 8q^{29} - 3q^{31} + 7q^{32} - 4q^{35} - 3q^{37} + 38q^{38} + 12q^{40} - 10q^{41} - 6q^{43} + 5q^{44} - 27q^{47} + 12q^{49} - 23q^{50} + 30q^{52} + 12q^{53} - 6q^{55} + 48q^{56} + 18q^{58} - 30q^{59} + 12q^{62} - 36q^{64} + 16q^{65} - 6q^{67} + 60q^{68} - 24q^{70} + 30q^{71} + 12q^{73} - 78q^{74} + 6q^{76} + 26q^{77} - 12q^{79} - 19q^{80} - 18q^{83} - 3q^{85} - 14q^{86} + 6q^{88} - 41q^{89} + 21q^{91} - 30q^{92} - 3q^{94} + 13q^{95} - 3q^{97} - 61q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(189, [\chi])$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	$q$-expansion
189.2.g.a	$2$	$1.509$	$\Q(\sqrt{-3}) $	None	$1$	$0$	$2$	$1$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$
189.2.g.b	$10$	$1.509$	10.0.$\cdots$.1	None	$-2$	$0$	$8$	$-1$	$q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(189, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(189, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(63, [\chi])$$^{\oplus 2}$

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Degree 3	Degree 4
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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) 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	189.2.g

Level	$189$
Weight	$2$
Character orbit	189.g
Rep. character	$\chi_{189}(100,\cdot)$
Character field	$\Q(\zeta_{3})$
Dimension	$12$
Newform subspaces	$2$
Sturm bound	$48$
Trace bound	$1$

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
189.2.g.a	\(2\)	\(1.509\)	\(\Q(\sqrt{-3}) \)	None	\(1\)	\(0\)	\(2\)	\(1\)	\(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
189.2.g.b	\(10\)	\(1.509\)	10.0.\(\cdots\).1	None	\(-2\)	\(0\)	\(8\)	\(-1\)	\(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(1+\cdots)q^{5}+\cdots\)