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

• Label: 3900.1.cu
• Level: $3900$
• Weight: $1$
• Character orbit: 3900.cu
• Rep. character: $\chi_{3900}(557,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $840$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3900.cu (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(840\)
Trace bound:			\(21\)

Dimensions

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

	Total	New	Old
Modular forms	184	16	168
Cusp forms	40	16	24
Eisenstein series	144	0	144

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 8 q^{19} + 4 q^{21} + 8 q^{31} - 8 q^{49} + 8 q^{81} - 4 q^{91}+O(q^{100}) \)

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.cu.a	$3900$	$1$	3900.cu	195.ac	$12$	$8$	$2$	$1.946$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓			3900.1.cu.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{24}^{7}q^{3}+(\zeta_{24}^{7}+\zeta_{24}^{9})q^{7}-\zeta_{24}^{2}q^{9}+\cdots\)
3900.1.cu.b	$3900$	$1$	3900.cu	195.ac	$12$	$8$	$2$	$1.946$	\(\Q(\zeta_{24})\)	$D_{12}$	\(\Q(\sqrt{-3}) \)	None		✓			3900.1.cu.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{24}^{7}q^{3}+(\zeta_{24}^{5}+\zeta_{24}^{11})q^{7}-\zeta_{24}^{2}q^{9}+\cdots\)

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

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