LMFDB - Space of modular forms of level 1110, weight 2, and Character 1110.x

Defining parameters

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$ 37 $
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$ 5 $
Sturm bound:			$456$
Trace bound:			$13$
Distinguishing $T_p$:			$7$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(1110, [\chi])$.

	Total	New	Old
Modular forms	472	56	416
Cusp forms	440	56	384
Eisenstein series	32	0	32

Trace form

$ 56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} + O(q^{10}) $

$ 56q - 4q^{3} + 28q^{4} - 4q^{7} - 28q^{9} - 8q^{10} - 8q^{11} + 4q^{12} - 12q^{13} - 28q^{16} - 12q^{19} - 4q^{21} + 28q^{25} - 8q^{26} + 8q^{27} + 4q^{28} - 4q^{30} + 16q^{33} + 12q^{34} + 24q^{35} - 56q^{36} + 16q^{37} + 16q^{38} + 24q^{39} - 4q^{40} + 24q^{42} - 4q^{44} - 4q^{46} + 32q^{47} + 8q^{48} - 56q^{49} - 12q^{52} - 8q^{53} - 12q^{55} - 24q^{58} + 36q^{59} + 8q^{63} - 56q^{64} + 4q^{65} - 12q^{67} + 8q^{70} + 8q^{71} - 8q^{73} - 12q^{74} - 8q^{75} - 12q^{76} - 8q^{77} - 8q^{78} + 12q^{79} - 28q^{81} + 48q^{83} - 8q^{84} + 32q^{85} - 8q^{86} + 24q^{87} + 36q^{89} + 4q^{90} - 12q^{91} - 24q^{92} - 84q^{93} + 24q^{94} - 16q^{95} - 48q^{98} + 4q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(1110, [\chi])$ 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
1110.2.x.a	$4$	$8.863$	$\Q(\zeta_{12})$	None	$0$	$2$	$0$	$2$	$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots$
1110.2.x.b	$4$	$8.863$	$\Q(\zeta_{12})$	None	$0$	$2$	$0$	$2$	$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots$
1110.2.x.c	$16$	$8.863$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	$0$	$-8$	$0$	$-2$	$q+(-\beta _{6}+\beta _{10})q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\cdots$
1110.2.x.d	$16$	$8.863$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$-8$	$0$	$-2$	$q+(\beta _{3}+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{9}q^{4}+\beta _{3}q^{5}+\cdots$
1110.2.x.e	$16$	$8.863$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	$0$	$8$	$0$	$-4$	$q+\beta _{6}q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{7}q^{5}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(1110, [\chi])$ into lower level spaces

$ S_{2}^{\mathrm{old}}(1110, [\chi]) \cong $ $S_{2}^{\mathrm{new}}(37, [\chi])$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(74, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(111, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(185, [\chi])$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(222, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(370, [\chi])$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(555, [\chi])$$^{\oplus 2}$

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$\zeta$ zeros

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(456\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) 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	1110.2.x

Level	$1110$
Weight	$2$
Character orbit	1110.x
Rep. character	$\chi_{1110}(751,\cdot)$
Character field	$\Q(\zeta_{6})$
Dimension	$56$
Newform subspaces	$5$
Sturm bound	$456$
Trace bound	$13$

Label	Dim.	\(A\)	Field	CM	Traces				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	$q$-expansion
1110.2.x.a	\(4\)	\(8.863\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots\)
1110.2.x.b	\(4\)	\(8.863\)	\(\Q(\zeta_{12})\)	None	\(0\)	\(2\)	\(0\)	\(2\)	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}+\zeta_{12}^{2}q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
1110.2.x.c	\(16\)	\(8.863\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	\(0\)	\(-8\)	\(0\)	\(-2\)	\(q+(-\beta _{6}+\beta _{10})q^{2}+\beta _{9}q^{3}-\beta _{9}q^{4}+\cdots\)
1110.2.x.d	\(16\)	\(8.863\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(-8\)	\(0\)	\(-2\)	\(q+(\beta _{3}+\beta _{5})q^{2}-\beta _{9}q^{3}+\beta _{9}q^{4}+\beta _{3}q^{5}+\cdots\)
1110.2.x.e	\(16\)	\(8.863\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	\(0\)	\(8\)	\(0\)	\(-4\)	\(q+\beta _{6}q^{2}-\beta _{1}q^{3}-\beta _{1}q^{4}-\beta _{7}q^{5}+\cdots\)