Space of modular forms of level 1936, weight 2, and Character 1936.e

• Label: 1936.2.e
• Level: $1936$
• Weight: $2$
• Character orbit: 1936.e
• Rep. character: $\chi_{1936}(1935,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $7$
• Sturm bound: $528$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1936.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 44 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(528\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1936, [\chi])\).

	Total	New	Old
Modular forms	300	54	246
Cusp forms	228	54	174
Eisenstein series	72	0	72

Trace form

\( 54 q - 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1936, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1936.2.e.a	$1936$	$2$	1936.e	44.c	$2$	$2$	$2$	$15.459$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-1}) \)		✓			1936.2.e.a	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{5}+3q^{9}+5\beta q^{13}-3\beta q^{17}+\cdots\)
1936.2.e.b	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	\(\Q(\sqrt{-2}, \sqrt{-7})\)	None		✓			1936.2.e.b	$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-3q^{5}-\beta _{1}q^{7}-4q^{9}-2\beta _{2}q^{13}+\cdots\)
1936.2.e.c	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	\(\Q(\sqrt{-2}, \sqrt{3})\)	\(\Q(\sqrt{-1}) \)		✓			1936.2.e.c	$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$11$	$\mathrm{U}(1)[D_{2}]$	\(q+(-2+\beta _{1})q^{5}+3q^{9}+\beta _{2}q^{13}+(-\beta _{2}+\cdots)q^{17}+\cdots\)
1936.2.e.d	$1936$	$2$	1936.e	44.c	$2$	$4$	$4$	$15.459$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		✓			1936.2.e.d	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+q^{5}-\beta _{3}q^{7}+4\beta _{1}q^{13}+\cdots\)
1936.2.e.e	$1936$	$2$	1936.e	44.c	$2$	$8$	$8$	$15.459$	8.0.484000000.6	None					176.2.q.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{5}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots\)
1936.2.e.f	$1936$	$2$	1936.e	44.c	$2$	$16$	$16$	$15.459$	16.0.\(\cdots\).1	None					176.2.q.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}-\beta _{13})q^{3}+(\beta _{5}+\beta _{12})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1936.2.e.g	$1936$	$2$	1936.e	44.c	$2$	$16$	$16$	$15.459$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1936.2.e.g	$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{12}\cdot 3^{2}\cdot 11^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-\beta _{11}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1936, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(968, [\chi])\)\(^{\oplus 2}\)