Space of modular forms of level 3064, weight 2, and trivial character

• Label: 3064.2.a
• Level: $3064$
• Weight: $2$
• Character orbit: 3064.a
• Rep. character: $\chi_{3064}(1,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $6$
• Sturm bound: $768$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3064 = 2^{3} \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3064.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(768\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3064))\).

	Total	New	Old
Modular forms	388	96	292
Cusp forms	381	96	285
Eisenstein series	7	0	7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(383\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(21\)
\(+\)	\(-\)	\(-\)	\(27\)
\(-\)	\(+\)	\(-\)	\(27\)
\(-\)	\(-\)	\(+\)	\(21\)
Plus space		\(+\)	\(42\)
Minus space		\(-\)	\(54\)

Trace form

96 * q - 2 * q^5 + 92 * q^9 + 2 * q^11 - 2 * q^13 + 12 * q^15 - 4 * q^17 - 4 * q^19 + 8 * q^21 - 4 * q^23 + 96 * q^25 + 8 * q^29 - 12 * q^31 - 4 * q^33 - 4 * q^35 - 10 * q^37 + 16 * q^39 - 4 * q^41 + 2 * q^45 + 8 * q^47 + 84 * q^49 + 12 * q^51 + 14 * q^53 - 8 * q^55 - 28 * q^57 + 14 * q^59 - 6 * q^61 + 36 * q^63 - 16 * q^67 + 12 * q^71 - 4 * q^73 - 28 * q^77 - 24 * q^79 + 80 * q^81 - 10 * q^83 - 4 * q^85 + 28 * q^87 + 4 * q^89 - 36 * q^91 - 28 * q^93 + 36 * q^95 - 12 * q^97 + 38 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3064))\) 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					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	383
3064.2.a.a	$3064$	$2$	3064.a	1.a	$1$	$2$	$2$	$24.466$	\(\Q(\sqrt{21}) \)	None	✓	✓			3064.2.a.a	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-6\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-2+\beta )q^{5}-3q^{7}+(2+\beta )q^{9}+\cdots\)
3064.2.a.b	$3064$	$2$	3064.a	1.a	$1$	$3$	$3$	$24.466$	3.3.469.1	None	✓	✓			3064.2.a.b	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(-2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
3064.2.a.c	$3064$	$2$	3064.a	1.a	$1$	$19$	$19$	$24.466$	\(\mathbb{Q}[x]/(x^{19} - \cdots)\)	None	✓	✓	✓		3064.2.a.c	$1$	$1$	\(0\)	\(-4\)	\(-7\)	\(11\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{5}q^{5}+(-\beta _{8}-\beta _{10})q^{7}+\cdots\)
3064.2.a.d	$3064$	$2$	3064.a	1.a	$1$	$21$	$21$	$24.466$		None	✓	✓	✓	✓	3064.2.a.d	$1$	$1$	\(0\)	\(-5\)	\(-2\)	\(-11\)		$+$	$+$	$+$		$\mathrm{SU}(2)$
3064.2.a.e	$3064$	$2$	3064.a	1.a	$1$	$24$	$24$	$24.466$		None	✓	✓	✓		3064.2.a.e	$1$	$0$	\(0\)	\(0\)	\(11\)	\(-5\)		$-$	$+$	$-$		$\mathrm{SU}(2)$
3064.2.a.f	$3064$	$2$	3064.a	1.a	$1$	$27$	$27$	$24.466$		None	✓	✓	✓	✓	3064.2.a.f	$1$	$0$	\(0\)	\(7\)	\(0\)	\(13\)		$+$	$-$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3064))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3064)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(383))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(766))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1532))\)\(^{\oplus 2}\)