Space of modular forms of level 1740, weight 2, and Character 1740.bc

• Label: 1740.2.bc
• Level: $1740$
• Weight: $2$
• Character orbit: 1740.bc
• Rep. character: $\chi_{1740}(853,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $60$
• Newform subspaces: $3$
• Sturm bound: $720$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1740.bc (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1740, [\chi])\).

	Total	New	Old
Modular forms	744	60	684
Cusp forms	696	60	636
Eisenstein series	48	0	48

Trace form

60 * q - 60 * q^9 - 4 * q^13 - 8 * q^15 + 4 * q^25 - 8 * q^33 - 32 * q^35 - 8 * q^39 - 28 * q^41 + 36 * q^53 + 8 * q^55 + 16 * q^57 + 20 * q^61 + 20 * q^65 + 16 * q^67 + 16 * q^73 + 24 * q^77 - 8 * q^79 + 60 * q^81 - 32 * q^83 - 32 * q^85 + 8 * q^87 - 4 * q^89 + 56 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(1740, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1740.2.bc.a	$1740$	$2$	1740.bc	145.j	$4$	$2$	$1$	$13.894$	\(\Q(\sqrt{-1}) \)	None		✓			1740.2.bb.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-i q^{3}+(-i-2)q^{5}+(-2 i+2)q^{7}+\cdots\)
1740.2.bc.b	$1740$	$2$	1740.bc	145.j	$4$	$28$	$14$	$13.894$		None		✓			1740.2.bb.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
1740.2.bc.c	$1740$	$2$	1740.bc	145.j	$4$	$30$	$15$	$13.894$		None		✓	✓		1740.2.bb.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1740, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1740, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(580, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(870, [\chi])\)\(^{\oplus 2}\)