Space of modular forms of level 245, weight 4, and Character 245.b

• Label: 245.4.b
• Level: $245$
• Weight: $4$
• Character orbit: 245.b
• Rep. character: $\chi_{245}(99,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $7$
• Sturm bound: $112$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(112\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(245, [\chi])\).

	Total	New	Old
Modular forms	92	66	26
Cusp forms	76	56	20
Eisenstein series	16	10	6

Trace form

\( 56 q - 204 q^{4} - 6 q^{5} - 12 q^{6} - 424 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(245, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
245.4.b.a	$245$	$4$	245.b	5.b	$2$	$2$	$2$	$14.455$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-35}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-4\beta q^{3}+8q^{4}+5\beta q^{5}-53q^{9}+72q^{11}+\cdots\)
245.4.b.b	$245$	$4$	245.b	5.b	$2$	$4$	$4$	$14.455$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(-4\zeta_{8}^{2}+2\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
245.4.b.c	$245$	$4$	245.b	5.b	$2$	$8$	$8$	$14.455$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+\beta _{2}q^{3}+(-9-\beta _{1})q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
245.4.b.d	$245$	$4$	245.b	5.b	$2$	$10$	$10$	$14.455$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$2^{3}\cdot 7^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+\beta _{6}q^{3}+(-4+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
245.4.b.e	$245$	$4$	245.b	5.b	$2$	$10$	$10$	$14.455$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-3+\beta _{2})q^{4}-\beta _{6}q^{5}+\cdots\)
245.4.b.f	$245$	$4$	245.b	5.b	$2$	$10$	$10$	$14.455$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-3+\beta _{2})q^{4}+\beta _{6}q^{5}+\cdots\)
245.4.b.g	$245$	$4$	245.b	5.b	$2$	$12$	$12$	$14.455$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{2}q^{3}+(-4+\beta _{5})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(245, [\chi]) \cong \)