Space of modular forms of level 1827, weight 2, and trivial character

• Label: 1827.2.a
• Level: $1827$
• Weight: $2$
• Character orbit: 1827.a
• Rep. character: $\chi_{1827}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $20$
• Sturm bound: $480$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1827 = 3^{2} \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1827.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(480\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1827))\).

	Total	New	Old
Modular forms	248	70	178
Cusp forms	233	70	163
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	\(7\)	\(29\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	$+$	\(7\)
\(+\)	\(+\)	\(-\)	$-$	\(7\)
\(+\)	\(-\)	\(+\)	$-$	\(7\)
\(+\)	\(-\)	\(-\)	$+$	\(7\)
\(-\)	\(+\)	\(+\)	$-$	\(11\)
\(-\)	\(+\)	\(-\)	$+$	\(10\)
\(-\)	\(-\)	\(+\)	$+$	\(7\)
\(-\)	\(-\)	\(-\)	$-$	\(14\)
Plus space			\(+\)	\(31\)
Minus space			\(-\)	\(39\)

Trace form

\( 70 q + 2 q^{2} + 78 q^{4} + 4 q^{5} + 6 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1827))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	7	29
1827.2.a.a	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	\(\Q\)	None	✓	$1$	$0$	\(-1\)	\(0\)	\(-2\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}-2q^{5}+q^{7}+3q^{8}+2q^{10}+\cdots\)
1827.2.a.b	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	\(\Q\)	None	✓	$1$	$1$	\(-1\)	\(0\)	\(0\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{4}+q^{7}+3q^{8}-6q^{13}-q^{14}+\cdots\)
1827.2.a.c	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(-1\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}-q^{5}+q^{7}-3q^{8}-q^{10}+\cdots\)
1827.2.a.d	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	\(\Q\)	None	✓	$1$	$1$	\(1\)	\(0\)	\(2\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
1827.2.a.e	$1827$	$2$	1827.a	1.a	$1$	$1$	$1$	$14.589$	\(\Q\)	None	✓	$1$	$0$	\(2\)	\(0\)	\(4\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+2q^{4}+4q^{5}+q^{7}+8q^{10}+\cdots\)
1827.2.a.f	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(-4\)	\(0\)	\(0\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+2q^{4}-2\beta q^{5}-q^{7}+4\beta q^{10}+\cdots\)
1827.2.a.g	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	\(\Q(\sqrt{17}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{4}+(-2+\beta )q^{5}-q^{7}-3q^{8}+\cdots\)
1827.2.a.h	$1827$	$2$	1827.a	1.a	$1$	$2$	$2$	$14.589$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$0$	\(2\)	\(0\)	\(4\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2+\beta )q^{5}+\cdots\)
1827.2.a.i	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(-4\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
1827.2.a.j	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	None	✓	$1$	$1$	\(1\)	\(0\)	\(5\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(2-\beta _{1}-\beta _{2})q^{5}+\cdots\)
1827.2.a.k	$1827$	$2$	1827.a	1.a	$1$	$3$	$3$	$14.589$	3.3.148.1	None	✓	$1$	$0$	\(3\)	\(0\)	\(6\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
1827.2.a.l	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.4352.1	None	✓	$1$	$1$	\(-4\)	\(0\)	\(-4\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{1}+\beta _{3})q^{2}+(2+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1827.2.a.m	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.6224.1	None	✓	$1$	$1$	\(-2\)	\(0\)	\(-4\)	\(4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{3})q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
1827.2.a.n	$1827$	$2$	1827.a	1.a	$1$	$4$	$4$	$14.589$	4.4.14656.1	None	✓	$1$	$0$	\(2\)	\(0\)	\(2\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}-\beta _{3}q^{5}+\cdots\)
1827.2.a.o	$1827$	$2$	1827.a	1.a	$1$	$5$	$5$	$14.589$	5.5.2626356.1	None	✓	$1$	$0$	\(-2\)	\(0\)	\(-5\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{4})q^{5}+\cdots\)
1827.2.a.p	$1827$	$2$	1827.a	1.a	$1$	$5$	$5$	$14.589$	5.5.1280720.1	None	✓	$1$	$0$	\(1\)	\(0\)	\(4\)	\(-5\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{4})q^{5}+\cdots\)
1827.2.a.q	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(0\)	\(-8\)	\(7\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1827.2.a.r	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$1$	\(-3\)	\(0\)	\(-8\)	\(-7\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1827.2.a.s	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(3\)	\(0\)	\(8\)	\(-7\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1+\beta _{2}-\beta _{5}+\beta _{6})q^{4}+(1+\cdots)q^{5}+\cdots\)
1827.2.a.t	$1827$	$2$	1827.a	1.a	$1$	$7$	$7$	$14.589$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	$1$	$0$	\(5\)	\(0\)	\(8\)	\(7\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1-\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1827))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1827)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(203))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(609))\)\(^{\oplus 2}\)