Space of modular forms of level 240, weight 9, and Character 240.c

• Label: 240.9.c
• Level: $240$
• Weight: $9$
• Character orbit: 240.c
• Rep. character: $\chi_{240}(209,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $6$
• Sturm bound: $432$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(432\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(240, [\chi])\).

	Total	New	Old
Modular forms	396	98	298
Cusp forms	372	94	278
Eisenstein series	24	4	20

Trace form

94 * q - 2 * q^9 - 78782 * q^15 + 83780 * q^19 + 183968 * q^21 + 318686 * q^25 - 122748 * q^31 - 2399872 * q^39 + 390624 * q^45 - 66762850 * q^49 + 13722308 * q^51 - 24933376 * q^55 + 36730172 * q^61 - 20014308 * q^69 - 97913856 * q^75 + 86670212 * q^79 - 107006050 * q^81 - 6081604 * q^85 - 82825728 * q^91 - 109415552 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.9.c.a	$240$	$9$	240.c	15.d	$2$	$1$	$1$	$97.771$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.9.d.a	$2$	$0$	\(0\)	\(-81\)	\(625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{4}q^{3}+5^{4}q^{5}+3^{8}q^{9}-15^{4}q^{15}+\cdots\)
240.9.c.b	$240$	$9$	240.c	15.d	$2$	$1$	$1$	$97.771$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.9.d.a	$2$	$0$	\(0\)	\(81\)	\(-625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3^{4}q^{3}-5^{4}q^{5}+3^{8}q^{9}-15^{4}q^{15}+\cdots\)
240.9.c.c	$240$	$9$	240.c	15.d	$2$	$12$	$12$	$97.771$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None					15.9.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(4\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5})q^{5}+\cdots\)
240.9.c.d	$240$	$9$	240.c	15.d	$2$	$16$	$16$	$97.771$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					60.9.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{34}\cdot 3^{20}\cdot 5^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}+\beta _{6}q^{7}+(-922+\cdots)q^{9}+\cdots\)
240.9.c.e	$240$	$9$	240.c	15.d	$2$	$16$	$16$	$97.771$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					30.9.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{44}\cdot 3^{20}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{5})q^{5}+(-6\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
240.9.c.f	$240$	$9$	240.c	15.d	$2$	$48$	$48$	$97.771$		None			✓		120.9.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{9}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(240, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)