Space of modular forms of level 3432, weight 2, and Character 3432.g

• Label: 3432.2.g
• Level: $3432$
• Weight: $2$
• Character orbit: 3432.g
• Rep. character: $\chi_{3432}(1585,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $6$
• Sturm bound: $1344$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3432.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1344\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3432, [\chi])\).

	Total	New	Old
Modular forms	688	72	616
Cusp forms	656	72	584
Eisenstein series	32	0	32

Trace form

\( 72 q - 4 q^{3} + 72 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3432, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3432.2.g.a	$3432$	$2$	3432.g	13.b	$2$	$2$	$2$	$27.405$	\(\Q(\sqrt{-1}) \)	None		✓	3432.2.g.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2iq^{5}-2iq^{7}+q^{9}-iq^{11}+\cdots\)
3432.2.g.b	$3432$	$2$	3432.g	13.b	$2$	$2$	$2$	$27.405$	\(\Q(\sqrt{-1}) \)	None		✓	3432.2.g.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2iq^{5}+2iq^{7}+q^{9}-iq^{11}+\cdots\)
3432.2.g.c	$3432$	$2$	3432.g	13.b	$2$	$14$	$14$	$27.405$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	3432.2.g.c	$2$	$0$	\(0\)	\(-14\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-\beta _{5}+\beta _{13})q^{5}-\beta _{10}q^{7}+\cdots\)
3432.2.g.d	$3432$	$2$	3432.g	13.b	$2$	$14$	$14$	$27.405$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		✓	3432.2.g.d	$2$	$0$	\(0\)	\(14\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}-\beta _{7}q^{7}+q^{9}+\beta _{8}q^{11}+\cdots\)
3432.2.g.e	$3432$	$2$	3432.g	13.b	$2$	$20$	$20$	$27.405$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	3432.2.g.e	$2$	$0$	\(0\)	\(-20\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}-\beta _{19}q^{7}+q^{9}-\beta _{6}q^{11}+\cdots\)
3432.2.g.f	$3432$	$2$	3432.g	13.b	$2$	$20$	$20$	$27.405$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	3432.2.g.f	$2$	$0$	\(0\)	\(20\)	\(0\)	\(0\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{15}q^{5}-\beta _{14}q^{7}+q^{9}-\beta _{11}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3432, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(429, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(858, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1716, [\chi])\)\(^{\oplus 2}\)