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

• Label: 2340.2.r
• Level: $2340$
• Weight: $2$
• Character orbit: 2340.r
• Rep. character: $\chi_{2340}(781,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $1008$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	1032	96	936
Cusp forms	984	96	888
Eisenstein series	48	0	48

Trace form

96 * q - 4 * q^3 - 4 * q^5 - 8 * q^9 + 4 * q^11 - 8 * q^17 - 24 * q^19 + 4 * q^21 - 12 * q^23 - 48 * q^25 + 20 * q^27 + 4 * q^29 - 20 * q^33 + 32 * q^41 + 12 * q^43 + 8 * q^45 - 36 * q^49 - 4 * q^51 + 32 * q^53 - 8 * q^57 - 16 * q^59 + 12 * q^61 + 48 * q^63 - 8 * q^65 + 12 * q^67 - 44 * q^69 - 64 * q^71 - 24 * q^73 - 4 * q^75 + 28 * q^77 - 8 * q^81 - 48 * q^83 - 48 * q^87 + 8 * q^89 - 4 * q^93 + 12 * q^97 - 4 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2340.2.r.a	$2340$	$2$	2340.r	9.c	$3$	$2$	$1$	$18.685$	\(\Q(\sqrt{-3}) \)	None		✓			2340.2.r.a	$2$	$1$	\(0\)	\(-3\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
2340.2.r.b	$2340$	$2$	2340.r	9.c	$3$	$2$	$1$	$18.685$	\(\Q(\sqrt{-3}) \)	None		✓			2340.2.r.b	$2$	$0$	\(0\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
2340.2.r.c	$2340$	$2$	2340.r	9.c	$3$	$2$	$1$	$18.685$	\(\Q(\sqrt{-3}) \)	None		✓			2340.2.r.c	$2$	$0$	\(0\)	\(3\)	\(-1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots\)
2340.2.r.d	$2340$	$2$	2340.r	9.c	$3$	$14$	$7$	$18.685$	\(\mathbb{Q}[x]/(x^{14} - \cdots)\)	None		✓			2340.2.r.d	$2$	$0$	\(0\)	\(2\)	\(7\)	\(-4\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{7})q^{3}-\beta _{4}q^{5}+(-1-\beta _{4}+\cdots)q^{7}+\cdots\)
2340.2.r.e	$2340$	$2$	2340.r	9.c	$3$	$20$	$10$	$18.685$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			2340.2.r.e	$2$	$0$	\(0\)	\(-4\)	\(-10\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{3}+(-1-\beta _{7})q^{5}+\beta _{15}q^{7}+\cdots\)
2340.2.r.f	$2340$	$2$	2340.r	9.c	$3$	$26$	$13$	$18.685$		None		✓			2340.2.r.f	$2$	$0$	\(0\)	\(-1\)	\(13\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$
2340.2.r.g	$2340$	$2$	2340.r	9.c	$3$	$30$	$15$	$18.685$		None		✓	✓		2340.2.r.g	$2$	$0$	\(0\)	\(-1\)	\(-15\)	\(0\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(2340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)