Space of modular forms of level 104, weight 2, and trivial character

• Label: 104.2.a
• Level: $104$
• Weight: $2$
• Character orbit: 104.a
• Rep. character: $\chi_{104}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(104))\).

	Total	New	Old
Modular forms	18	3	15
Cusp forms	11	3	8
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.

\(2\)	\(13\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(3\)	\(0\)	\(3\)		\(2\)	\(0\)	\(2\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(6\)	\(2\)	\(4\)		\(4\)	\(2\)	\(2\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(6\)	\(1\)	\(5\)		\(4\)	\(1\)	\(3\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(3\)	\(0\)	\(3\)		\(1\)	\(0\)	\(1\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(6\)	\(0\)	\(6\)		\(3\)	\(0\)	\(3\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(12\)	\(3\)	\(9\)		\(8\)	\(3\)	\(5\)		\(4\)	\(0\)	\(4\)

Trace form

3 * q + 2 * q^3 + 2 * q^5 + 4 * q^7 + q^9 - 4 * q^11 + q^13 - 8 * q^15 - 4 * q^17 - 4 * q^21 - 12 * q^23 - q^25 + 2 * q^27 - 10 * q^29 + 4 * q^31 - 20 * q^33 + 2 * q^35 + 18 * q^37 + 10 * q^41 + 14 * q^43 - 2 * q^45 - 4 * q^47 + 13 * q^49 + 22 * q^51 - 14 * q^53 + 16 * q^55 + 16 * q^57 + 8 * q^59 + 14 * q^61 - 20 * q^63 + 4 * q^65 + 4 * q^67 - 4 * q^69 + 4 * q^71 - 14 * q^73 - 28 * q^75 + 8 * q^77 + 28 * q^79 - 13 * q^81 - 28 * q^83 - 24 * q^85 - 8 * q^87 + 10 * q^89 - 6 * q^91 - 12 * q^95 - 10 * q^97 - 16 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(104))\) 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	13
104.2.a.a	$104$	$2$	104.a	1.a	$1$	$1$	$1$	$0.830$	\(\Q\)	None	✓	✓	✓	✓	104.2.a.a	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(5\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-q^{5}+5q^{7}-2q^{9}-2q^{11}+\cdots\)
104.2.a.b	$104$	$2$	104.a	1.a	$1$	$2$	$2$	$0.830$	\(\Q(\sqrt{17}) \)	None	✓	✓	✓	✓	104.2.a.b	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(2-\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(104)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)