Space of modular forms of level 2800, weight 2, and Character 2800.k

• Label: 2800.2.k
• Level: $2800$
• Weight: $2$
• Character orbit: 2800.k
• Rep. character: $\chi_{2800}(2351,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $16$
• Sturm bound: $960$
• Trace bound: $37$

Defining parameters

Level:	\( N \)	\(=\)	\( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2800.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(960\)
Trace bound:			\(37\)
Distinguishing \(T_p\):			\(3\), \(11\), \(19\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2800, [\chi])\).

	Total	New	Old
Modular forms	516	76	440
Cusp forms	444	76	368
Eisenstein series	72	0	72

Trace form

\( 76 q + 76 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2800, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2800.2.k.a	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+(2-\zeta_{6})q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
2800.2.k.b	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+(2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
2800.2.k.c	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2q^{3}+(2+\zeta_{6})q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
2800.2.k.d	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+(-2-\zeta_{6})q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots\)
2800.2.k.e	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+(-2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
2800.2.k.f	$2800$	$2$	2800.k	28.d	$2$	$2$	$2$	$22.358$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{3}+(-2-\zeta_{6})q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\)
2800.2.k.g	$2800$	$2$	2800.k	28.d	$2$	$4$	$4$	$22.358$	\(\Q(\sqrt{2}, \sqrt{-5})\)	\(\Q(\sqrt{-5}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{1}-\beta _{2})q^{7}-q^{9}+(-3+\cdots)q^{21}+\cdots\)
2800.2.k.h	$2800$	$2$	2800.k	28.d	$2$	$4$	$4$	$22.358$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}-q^{9}+\beta _{3}q^{11}+\cdots\)
2800.2.k.i	$2800$	$2$	2800.k	28.d	$2$	$4$	$4$	$22.358$	\(\Q(\sqrt{2}, \sqrt{-5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{7}-q^{9}-\beta _{3}q^{11}+\cdots\)
2800.2.k.j	$2800$	$2$	2800.k	28.d	$2$	$4$	$4$	$22.358$	\(\Q(\sqrt{-5}, \sqrt{7})\)	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{3}-\beta _{3}q^{7}+4q^{9}-\beta _{2}q^{11}+\cdots\)
2800.2.k.k	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	8.0.796594176.2	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{7}q^{7}-q^{9}-\beta _{2}q^{11}+\beta _{6}q^{13}+\cdots\)
2800.2.k.l	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	8.0.303595776.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{7}-\beta _{6}q^{9}+\cdots\)
2800.2.k.m	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{4}q^{7}+(1+\beta _{1})q^{9}-\beta _{7}q^{11}+\cdots\)
2800.2.k.n	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{3}+(\zeta_{24}+\cdots)q^{7}+\cdots\)
2800.2.k.o	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}-\zeta_{24}^{5}+\zeta_{24}^{6})q^{3}+(\zeta_{24}+\cdots)q^{7}+\cdots\)
2800.2.k.p	$2800$	$2$	2800.k	28.d	$2$	$8$	$8$	$22.358$	8.0.\(\cdots\).2	\(\Q(\sqrt{-35}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{6}q^{3}+(-\beta _{6}+\beta _{7})q^{7}+(3+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2800, [\chi]) \cong \)