Space of modular forms of level 240, weight 3, and Character 240.c

• Label: 240.3.c
• Level: $240$
• Weight: $3$
• Character orbit: 240.c
• Rep. character: $\chi_{240}(209,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $5$
• Sturm bound: $144$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(144\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(240, [\chi])\).

	Total	New	Old
Modular forms	108	26	82
Cusp forms	84	22	62
Eisenstein series	24	4	20

Trace form

22 * q - 2 * q^9 - 14 * q^15 + 20 * q^19 + 8 * q^21 - 10 * q^25 + 36 * q^31 + 32 * q^39 + 24 * q^45 - 154 * q^49 + 116 * q^51 - 64 * q^55 + 140 * q^61 + 36 * q^69 - 192 * q^75 - 28 * q^79 - 154 * q^81 + 44 * q^85 - 384 * q^91 - 32 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
240.3.c.a	$240$	$3$	240.c	15.d	$2$	$1$	$1$	$6.540$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3q^{3}-5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots\)
240.3.c.b	$240$	$3$	240.c	15.d	$2$	$1$	$1$	$6.540$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓				15.3.d.a	$2$	$0$	\(0\)	\(3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+3q^{3}+5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots\)
240.3.c.c	$240$	$3$	240.c	15.d	$2$	$4$	$4$	$6.540$	\(\Q(\sqrt{2}, \sqrt{-17})\)	None					30.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2\beta _{2}+\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
240.3.c.d	$240$	$3$	240.c	15.d	$2$	$4$	$4$	$6.540$	\(\Q(i, \sqrt{5})\)	None					60.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
240.3.c.e	$240$	$3$	240.c	15.d	$2$	$12$	$12$	$6.540$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None			✓		120.3.c.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(240, [\chi])\) into lower level spaces

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