Space of modular forms of level 2240, weight 2, and Character 2240.k

• Label: 2240.2.k
• Level: $2240$
• Weight: $2$
• Character orbit: 2240.k
• Rep. character: $\chi_{2240}(1791,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $768$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(768\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2240, [\chi])\).

	Total	New	Old
Modular forms	408	64	344
Cusp forms	360	64	296
Eisenstein series	48	0	48

Trace form

\( 64 q + 64 q^{9} - 16 q^{21} - 64 q^{25} + 16 q^{29} - 16 q^{37} - 16 q^{53} + 96 q^{81} + 32 q^{93}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2240, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2240.2.k.a	$2240$	$2$	2240.k	28.d	$2$	$4$	$4$	$17.886$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{3}-\beta_1 q^{5}+(\beta_{3}+2\beta_1)q^{7}+\cdots\)
2240.2.k.b	$2240$	$2$	2240.k	28.d	$2$	$4$	$4$	$17.886$	\(\Q(\zeta_{12})\)	None					140.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{3} q^{3}-\beta_1 q^{5}+(\beta_{3}-2\beta_1)q^{7}+\cdots\)
2240.2.k.c	$2240$	$2$	2240.k	28.d	$2$	$8$	$8$	$17.886$	8.0.303595776.1	None					560.2.k.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+\beta _{4}q^{5}+(-\beta _{1}+\beta _{5}+\beta _{6}+\cdots)q^{7}+\cdots\)
2240.2.k.d	$2240$	$2$	2240.k	28.d	$2$	$8$	$8$	$17.886$	8.0.\(\cdots\).7	None					560.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}-\beta _{3}q^{5}+(-\beta _{4}+\beta _{6})q^{7}+\cdots\)
2240.2.k.e	$2240$	$2$	2240.k	28.d	$2$	$8$	$8$	$17.886$	8.0.342102016.5	None					140.2.g.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{5})q^{3}+\beta _{1}q^{5}+(-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
2240.2.k.f	$2240$	$2$	2240.k	28.d	$2$	$16$	$16$	$17.886$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					1120.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
2240.2.k.g	$2240$	$2$	2240.k	28.d	$2$	$16$	$16$	$17.886$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					1120.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+\beta _{4}q^{5}+\beta _{11}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2240, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2240, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)