Space of modular forms of level 1400, weight 2, and Character 1400.bh

• Label: 1400.2.bh
• Level: $1400$
• Weight: $2$
• Character orbit: 1400.bh
• Rep. character: $\chi_{1400}(249,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $10$
• Sturm bound: $480$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(480\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1400, [\chi])\).

	Total	New	Old
Modular forms	528	72	456
Cusp forms	432	72	360
Eisenstein series	96	0	96

Trace form

\( 72 q + 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1400, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1400.2.bh.a	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2\zeta_{12}+3\zeta_{12}^{3})q^{7}+\cdots\)
1400.2.bh.b	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.c	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(3\zeta_{12}-2\zeta_{12}^{3})q^{7}-2\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.d	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{3}+(3\zeta_{12}-\zeta_{12}^{3})q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.e	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
1400.2.bh.f	$1400$	$2$	1400.bh	35.j	$6$	$4$	$2$	$11.179$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{3}+(2\zeta_{12}+\zeta_{12}^{3})q^{7}+6\zeta_{12}^{2}q^{9}+\cdots\)
1400.2.bh.g	$1400$	$2$	1400.bh	35.j	$6$	$8$	$4$	$11.179$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{7}+\cdots\)
1400.2.bh.h	$1400$	$2$	1400.bh	35.j	$6$	$12$	$6$	$11.179$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{7}+\zeta_{36}^{11})q^{3}+\cdots\)
1400.2.bh.i	$1400$	$2$	1400.bh	35.j	$6$	$12$	$6$	$11.179$	12.0.\(\cdots\).37	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5}+\beta _{7}+\beta _{8})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1400.2.bh.j	$1400$	$2$	1400.bh	35.j	$6$	$16$	$8$	$11.179$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{9})q^{3}+(\beta _{6}-\beta _{7})q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1400, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1400, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)