Space of modular forms of level 3636, weight 1, and Character 3636.m

• Label: 3636.1.m
• Level: $3636$
• Weight: $1$
• Character orbit: 3636.m
• Rep. character: $\chi_{3636}(1909,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $612$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3636 = 2^{2} \cdot 3^{2} \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3636.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 101 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(612\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3636, [\chi])\).

	Total	New	Old
Modular forms	36	6	30
Cusp forms	12	6	6
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	6	0

Trace form

\( 6 q - 2 q^{5} + 2 q^{7} + 2 q^{11} + 6 q^{19} - 6 q^{31} - 2 q^{35} - 8 q^{37} + 2 q^{53} + 2 q^{55} + 2 q^{59} - 4 q^{61} - 2 q^{67} - 2 q^{71} + 6 q^{79} + 2 q^{89} + 2 q^{91} - 2 q^{95} - 4 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3636, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3636.1.m.a	$3636$	$1$	3636.m	101.c	$4$	$2$	$1$	$1.815$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		✓			3636.1.m.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-q^{5}+(-i-1)q^{11}+i q^{13}-i q^{17}+\cdots\)
3636.1.m.b	$3636$	$1$	3636.m	101.c	$4$	$2$	$1$	$1.815$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None					404.1.f.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(2\)	$1$		\(q-q^{5}+(i+1)q^{7}+(i+1)q^{11}-i q^{13}+\cdots\)
3636.1.m.c	$3636$	$1$	3636.m	101.c	$4$	$2$	$1$	$1.815$	\(\Q(\sqrt{-1}) \)	$S_{4}$	None	None		✓			3636.1.m.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+q^{5}+(i+1)q^{11}+i q^{13}+i q^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3636, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3636, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(404, [\chi])\)\(^{\oplus 3}\)