Space of modular forms of level 3900, weight 1, and Character 3900.ca

• Label: 3900.1.ca
• Level: $3900$
• Weight: $1$
• Character orbit: 3900.ca
• Rep. character: $\chi_{3900}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $840$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3900.ca (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(840\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3900, [\chi])\).

	Total	New	Old
Modular forms	96	6	90
Cusp forms	24	6	18
Eisenstein series	72	0	72

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - q^{3} + 3 q^{7} - 3 q^{9} - q^{13} + 6 q^{19} + 2 q^{27} - q^{43} - 3 q^{61} - 3 q^{63} - 3 q^{67} + 6 q^{79} - 3 q^{81} - 3 q^{91} + 3 q^{93} + 3 q^{97}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3900.1.ca.a	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3900.1.ca.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)
3900.1.ca.b	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None					156.1.s.a	$4$	$0$	\(0\)	\(-1\)	\(0\)	\(3\)	$1$		\(q+\zeta_{6}^{2}q^{3}+(1-\zeta_{6}^{2})q^{7}-\zeta_{6}q^{9}-\zeta_{6}q^{13}+\cdots\)
3900.1.ca.c	$3900$	$1$	3900.ca	39.h	$6$	$2$	$1$	$1.946$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-3}) \)	None		✓			3900.1.ca.a	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+(1-\zeta_{6}^{2}+\cdots)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3900, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 3}\)