Space of modular forms of level 3744, weight 2, and Character 3744.m

• Label: 3744.2.m
• Level: $3744$
• Weight: $2$
• Character orbit: 3744.m
• Rep. character: $\chi_{3744}(1585,\cdot)$
• Character field: $\Q$
• Dimension: $68$
• Newform subspaces: $9$
• Sturm bound: $1344$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3744.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1344\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).

	Total	New	Old
Modular forms	704	72	632
Cusp forms	640	68	572
Eisenstein series	64	4	60

Trace form

\( 68 q + 8 q^{23} + 52 q^{25} - 76 q^{49} + 24 q^{55} + 24 q^{65} - 16 q^{79} - 96 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3744.2.m.a	$3744$	$2$	3744.m	104.e	$2$	$2$	$2$	$29.896$	\(\Q(\sqrt{-1}) \)	None					312.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{5}+4 q^{11}+(\beta-3)q^{13}+6 q^{17}+\cdots\)
3744.2.m.b	$3744$	$2$	3744.m	104.e	$2$	$2$	$2$	$29.896$	\(\Q(\sqrt{-1}) \)	None					104.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{5}-3 i q^{7}+2 q^{11}+(-2 i-3)q^{13}+\cdots\)
3744.2.m.c	$3744$	$2$	3744.m	104.e	$2$	$2$	$2$	$29.896$	\(\Q(\sqrt{-1}) \)	None					104.2.e.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{5}-3 i q^{7}-2 q^{11}+(2 i+3)q^{13}+\cdots\)
3744.2.m.d	$3744$	$2$	3744.m	104.e	$2$	$2$	$2$	$29.896$	\(\Q(\sqrt{-1}) \)	None					312.2.m.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{5}-4 q^{11}+(-\beta+3)q^{13}+6 q^{17}+\cdots\)
3744.2.m.e	$3744$	$2$	3744.m	104.e	$2$	$4$	$4$	$29.896$	\(\Q(\sqrt{-2}, \sqrt{13})\)	\(\Q(\sqrt{-78}) \)					936.2.m.e	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{13}-2\beta _{2}q^{19}-5q^{25}-\beta _{3}q^{29}+\cdots\)
3744.2.m.f	$3744$	$2$	3744.m	104.e	$2$	$8$	$8$	$29.896$	8.0.\(\cdots\).21	\(\Q(\sqrt{-39}) \)					936.2.m.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{2}+\beta _{6})q^{11}-\beta _{1}q^{13}+\cdots\)
3744.2.m.g	$3744$	$2$	3744.m	104.e	$2$	$8$	$8$	$29.896$	8.0.4521217600.1	None					104.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{5}-\beta _{3}q^{7}+(\beta _{4}+\beta _{6})q^{11}+(-\beta _{6}+\cdots)q^{13}+\cdots\)
3744.2.m.h	$3744$	$2$	3744.m	104.e	$2$	$16$	$16$	$29.896$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					936.2.m.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{20}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{14}q^{5}+\beta _{5}q^{7}+(-\beta _{11}+\beta _{14}+\cdots)q^{11}+\cdots\)
3744.2.m.i	$3744$	$2$	3744.m	104.e	$2$	$24$	$24$	$29.896$		None			✓		312.2.m.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)