Space of modular forms of level 1936, weight 1, and Character 1936.n

• Label: 1936.1.n
• Level: $1936$
• Weight: $1$
• Character orbit: 1936.n
• Rep. character: $\chi_{1936}(161,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $264$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1936 = 2^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1936.n (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(264\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1936, [\chi])\).

	Total	New	Old
Modular forms	184	28	156
Cusp forms	40	12	28
Eisenstein series	144	16	128

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	8	0

Trace form

\( 12 q - 3 q^{3} - q^{5} - q^{15} + 12 q^{23} + 3 q^{27} + q^{31} - q^{37} + 2 q^{47} + q^{49} - 2 q^{53} + q^{59} - 4 q^{67} - 3 q^{69} - 3 q^{71} + 3 q^{81} - 12 q^{89} + q^{93} + 3 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1936, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1936.1.n.a	$1936$	$1$	1936.n	11.d	$10$	$4$	$1$	$0.966$	\(\Q(\zeta_{10})\)	$D_{3}$	\(\Q(\sqrt{-11}) \)	None					44.1.d.a	$8$	$0$	\(0\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-\zeta_{10}^{3}q^{3}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{15}+\cdots\)
1936.1.n.b	$1936$	$1$	1936.n	11.d	$10$	$8$	$2$	$0.966$	8.0.64000000.1	$S_{4}$	None	None			✓		968.1.h.a	$8$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$		\(q-\beta _{6}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{6})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1936, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1936, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(968, [\chi])\)\(^{\oplus 2}\)