Space of modular forms of level 2340, weight 2, and Character 2340.u

• Label: 2340.2.u
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.u
• Rep. character: $\chi_{2340}(73,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $70$
• Newform subspaces: $9$
• Sturm bound: $1008$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2340.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1008\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).

	Total	New	Old
Modular forms	1056	70	986
Cusp forms	960	70	890
Eisenstein series	96	0	96

Trace form

\( 70 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2340.2.u.a	$2340$	$2$	2340.u	65.k	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1-2i)q^{5}+4iq^{7}+(2-2i)q^{11}+\cdots\)
2340.2.u.b	$2340$	$2$	2340.u	65.k	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+2i)q^{5}+4iq^{7}+(-2+2i)q^{11}+\cdots\)
2340.2.u.c	$2340$	$2$	2340.u	65.k	$4$	$2$	$1$	$18.685$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-2i)q^{5}-4iq^{7}+(4-4i)q^{11}+\cdots\)
2340.2.u.d	$2340$	$2$	2340.u	65.k	$4$	$4$	$2$	$18.685$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{7}+\zeta_{8}q^{11}+\cdots\)
2340.2.u.e	$2340$	$2$	2340.u	65.k	$4$	$4$	$2$	$18.685$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{8}+2\zeta_{8}^{3})q^{5}+3\zeta_{8}^{2}q^{7}+\zeta_{8}^{3}q^{11}+\cdots\)
2340.2.u.f	$2340$	$2$	2340.u	65.k	$4$	$4$	$2$	$18.685$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2340.2.u.g	$2340$	$2$	2340.u	65.k	$4$	$8$	$4$	$18.685$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{3}+\beta _{6})q^{5}+(\beta _{4}+\beta _{5})q^{7}+(-2+\cdots)q^{11}+\cdots\)
2340.2.u.h	$2340$	$2$	2340.u	65.k	$4$	$16$	$8$	$18.685$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{8}q^{5}+(\beta _{6}+\beta _{9})q^{7}+(-\beta _{7}+\beta _{8}+\cdots)q^{11}+\cdots\)
2340.2.u.i	$2340$	$2$	2340.u	65.k	$4$	$28$	$14$	$18.685$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)