Space of modular forms of level 25, weight 18, and Character 25.b

• Label: 25.18.b
• Level: $25$
• Weight: $18$
• Character orbit: 25.b
• Rep. character: $\chi_{25}(24,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(25, [\chi])\).

	Total	New	Old
Modular forms	46	26	20
Cusp forms	40	24	16
Eisenstein series	6	2	4

Trace form

\( 24 q - 1332178 q^{4} + 2905738 q^{6} - 1000861012 q^{9} + O(q^{10}) \)

Decomposition of \(S_{18}^{\mathrm{new}}(25, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
25.18.b.a	$25$	$18$	25.b	5.b	$2$	$2$	$2$	$45.806$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+264iq^{2}-2142iq^{3}-147712q^{4}+\cdots\)
25.18.b.b	$25$	$18$	25.b	5.b	$2$	$4$	$4$	$45.806$	\(\Q(i, \sqrt{39})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{4}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(34\beta _{1}+\beta _{3})q^{2}+(549\beta _{1}+52\beta _{3})q^{3}+\cdots\)
25.18.b.c	$25$	$18$	25.b	5.b	$2$	$6$	$6$	$45.806$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{9}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-8\beta _{1}-105\beta _{2}+\cdots)q^{3}+\cdots\)
25.18.b.d	$25$	$18$	25.b	5.b	$2$	$12$	$12$	$45.806$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}\cdot 3^{6}\cdot 5^{36}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+(-9\beta _{6}-\beta _{8})q^{3}+(-71886+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(25, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(25, [\chi]) \cong \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)