Space of modular forms of level 15, weight 2, and trivial character

• Label: 15.2.a
• Level: $15$
• Weight: $2$
• Character orbit: 15.a
• Rep. character: $\chi_{15}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(15))\).

	Total	New	Old
Modular forms	4	1	3
Cusp forms	1	1	0
Eisenstein series	3	0	3

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

\(3\)	\(5\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(-\)	\(-\)		\(2\)	\(1\)	\(1\)		\(1\)	\(1\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(3\)	\(1\)	\(2\)		\(1\)	\(1\)	\(0\)		\(2\)	\(0\)	\(2\)

Trace form

q - q^2 - q^3 - q^4 + q^5 + q^6 + 3 * q^8 + q^9 - q^10 - 4 * q^11 + q^12 - 2 * q^13 - q^15 - q^16 + 2 * q^17 - q^18 + 4 * q^19 - q^20 + 4 * q^22 - 3 * q^24 + q^25 + 2 * q^26 - q^27 - 2 * q^29 + q^30 - 5 * q^32 + 4 * q^33 - 2 * q^34 - q^36 - 10 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 10 * q^41 + 4 * q^43 + 4 * q^44 + q^45 + 8 * q^47 + q^48 - 7 * q^49 - q^50 - 2 * q^51 + 2 * q^52 - 10 * q^53 + q^54 - 4 * q^55 - 4 * q^57 + 2 * q^58 - 4 * q^59 + q^60 - 2 * q^61 + 7 * q^64 - 2 * q^65 - 4 * q^66 + 12 * q^67 - 2 * q^68 - 8 * q^71 + 3 * q^72 + 10 * q^73 + 10 * q^74 - q^75 - 4 * q^76 - 2 * q^78 - q^80 + q^81 - 10 * q^82 + 12 * q^83 + 2 * q^85 - 4 * q^86 + 2 * q^87 - 12 * q^88 - 6 * q^89 - q^90 - 8 * q^94 + 4 * q^95 + 5 * q^96 + 2 * q^97 + 7 * q^98 - 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3	5
15.2.a.a	$15$	$2$	15.a	1.a	$1$	$1$	$1$	$0.120$	\(\Q\)	None	✓	✓	✓	✓	15.2.a.a	$1$	$0$	\(-1\)	\(-1\)	\(1\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)