Space of modular forms of level 3432, weight 2, and trivial character

• Label: 3432.2.a
• Level: $3432$
• Weight: $2$
• Character orbit: 3432.a
• Rep. character: $\chi_{3432}(1,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $24$
• Sturm bound: $1344$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3432 = 2^{3} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3432.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(1344\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3432))\).

	Total	New	Old
Modular forms	688	60	628
Cusp forms	657	60	597
Eisenstein series	31	0	31

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(3\)	\(11\)	\(13\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	$+$	\(4\)
\(+\)	\(+\)	\(+\)	\(-\)	$-$	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	$-$	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	$+$	\(3\)
\(+\)	\(-\)	\(+\)	\(+\)	$-$	\(5\)
\(+\)	\(-\)	\(+\)	\(-\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(+\)	$+$	\(2\)
\(+\)	\(-\)	\(-\)	\(-\)	$-$	\(6\)
\(-\)	\(+\)	\(+\)	\(+\)	$-$	\(3\)
\(-\)	\(+\)	\(+\)	\(-\)	$+$	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	$+$	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	$-$	\(3\)
\(-\)	\(-\)	\(+\)	\(+\)	$+$	\(3\)
\(-\)	\(-\)	\(+\)	\(-\)	$-$	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	$-$	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	$+$	\(3\)
Plus space				\(+\)	\(26\)
Minus space				\(-\)	\(34\)

Trace form

\( 60 q + 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3432))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3	11	13
3432.2.a.a	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.b	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-1\)	\(-1\)	\(3\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-q^{5}+3q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.c	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(4\)		$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+4q^{7}+q^{9}-q^{11}-q^{13}+8q^{17}+\cdots\)
3432.2.a.d	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(3\)		$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}+3q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.e	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-2\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{5}+q^{9}+q^{11}-q^{13}-2q^{15}+\cdots\)
3432.2.a.f	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(0\)		$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{9}+q^{11}-q^{13}-4q^{17}+\cdots\)
3432.2.a.g	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(0\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+q^{9}-q^{11}+q^{13}+2q^{15}+\cdots\)
3432.2.a.h	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}-q^{13}+\cdots\)
3432.2.a.i	$3432$	$2$	3432.a	1.a	$1$	$1$	$1$	$27.405$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(2\)	\(4\)		$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+2q^{5}+4q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
3432.2.a.j	$3432$	$2$	3432.a	1.a	$1$	$2$	$2$	$27.405$	\(\Q(\sqrt{6}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(-4\)	\(-4\)		$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(-2+\beta )q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.k	$3432$	$2$	3432.a	1.a	$1$	$2$	$2$	$27.405$	\(\Q(\sqrt{5}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)		$-$	$+$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1-\beta )q^{5}+q^{9}-q^{11}-q^{13}+\cdots\)
3432.2.a.l	$3432$	$2$	3432.a	1.a	$1$	$2$	$2$	$27.405$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(2\)	\(0\)		$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta )q^{5}+2\beta q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.m	$3432$	$2$	3432.a	1.a	$1$	$2$	$2$	$27.405$	\(\Q(\sqrt{2}) \)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-4\)		$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta q^{5}-2q^{7}+q^{9}-q^{11}+q^{13}+\cdots\)
3432.2.a.n	$3432$	$2$	3432.a	1.a	$1$	$3$	$3$	$27.405$	3.3.404.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(-4\)	\(-6\)		$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+(-1-\beta _{2})q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.o	$3432$	$2$	3432.a	1.a	$1$	$3$	$3$	$27.405$	3.3.892.1	None	✓	$1$	$0$	\(0\)	\(3\)	\(-1\)	\(5\)		$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{1}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+q^{9}+\cdots\)
3432.2.a.p	$3432$	$2$	3432.a	1.a	$1$	$3$	$3$	$27.405$	3.3.148.1	None	✓	$1$	$1$	\(0\)	\(3\)	\(0\)	\(-2\)		$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots\)
3432.2.a.q	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.22676.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(-3\)	\(3\)		$+$	$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
3432.2.a.r	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.70164.1	None	✓	$1$	$1$	\(0\)	\(-4\)	\(1\)	\(-1\)		$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
3432.2.a.s	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.29268.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(-2\)		$+$	$+$	$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
3432.2.a.t	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.23252.1	None	✓	$1$	$0$	\(0\)	\(-4\)	\(4\)	\(2\)		$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+(1+\beta _{2})q^{5}+\beta _{1}q^{7}+q^{9}+q^{11}+\cdots\)
3432.2.a.u	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.70164.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(1\)	\(1\)		$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+q^{9}+\cdots\)
3432.2.a.v	$3432$	$2$	3432.a	1.a	$1$	$4$	$4$	$27.405$	4.4.83476.1	None	✓	$1$	$0$	\(0\)	\(4\)	\(2\)	\(-2\)		$+$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{3}q^{5}+(-1+\beta _{1}+\beta _{3})q^{7}+\cdots\)
3432.2.a.w	$3432$	$2$	3432.a	1.a	$1$	$5$	$5$	$27.405$	5.5.2172244.1	None	✓	$1$	$1$	\(0\)	\(-5\)	\(1\)	\(-5\)		$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q-q^{3}+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}+q^{9}+\cdots\)
3432.2.a.x	$3432$	$2$	3432.a	1.a	$1$	$5$	$5$	$27.405$	5.5.46437524.1	None	✓	$1$	$0$	\(0\)	\(5\)	\(1\)	\(-3\)		$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+q^{3}+\beta _{1}q^{5}+(-1-\beta _{4})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3432))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3432)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(264))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(858))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1716))\)\(^{\oplus 2}\)