Space of modular forms of level 875, weight 2, and Character 875.f

• Label: 875.2.f
• Level: $875$
• Weight: $2$
• Character orbit: 875.f
• Rep. character: $\chi_{875}(307,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $128$
• Newform subspaces: $4$
• Sturm bound: $200$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(200\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(875, [\chi])\).

	Total	New	Old
Modular forms	220	128	92
Cusp forms	180	128	52
Eisenstein series	40	0	40

Trace form

\( 128 q + 4 q^{11} - 112 q^{16} + 24 q^{21} - 168 q^{36} + 112 q^{46} + 28 q^{51} - 28 q^{56} - 16 q^{71} - 104 q^{81} + 152 q^{86} - 176 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(875, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
875.2.f.a	$875$	$2$	875.f	35.f	$4$	$16$	$8$	$6.987$	16.0.\(\cdots\).4	\(\Q(\sqrt{-35}) \)		✓			875.2.f.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{8}$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{5}q^{3}-2\beta _{7}q^{4}-\beta _{14}q^{7}+(3\beta _{7}+\cdots)q^{9}+\cdots\)
875.2.f.b	$875$	$2$	875.f	35.f	$4$	$16$	$8$	$6.987$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			875.2.f.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{6}q^{2}+(-\beta _{3}-\beta _{12})q^{3}+(-3\beta _{7}+\cdots)q^{4}+\cdots\)
875.2.f.c	$875$	$2$	875.f	35.f	$4$	$32$	$16$	$6.987$		None		✓			875.2.f.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
875.2.f.d	$875$	$2$	875.f	35.f	$4$	$64$	$32$	$6.987$		None		✓	✓		875.2.f.d	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(875, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(875, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)