Space of modular forms of level 335, weight 2, and trivial character

• Label: 335.2.a
• Level: $335$
• Weight: $2$
• Character orbit: 335.a
• Rep. character: $\chi_{335}(1,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $5$
• Sturm bound: $68$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 335 = 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	335.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(68\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(335))\).

	Total	New	Old
Modular forms	36	23	13
Cusp forms	33	23	10
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.

\(5\)	\(67\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(4\)	\(2\)	\(2\)		\(4\)	\(2\)	\(2\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(13\)	\(9\)	\(4\)		\(12\)	\(9\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(14\)	\(11\)	\(3\)		\(13\)	\(11\)	\(2\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(5\)	\(1\)	\(4\)		\(4\)	\(1\)	\(3\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(9\)	\(3\)	\(6\)		\(8\)	\(3\)	\(5\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(27\)	\(20\)	\(7\)		\(25\)	\(20\)	\(5\)		\(2\)	\(0\)	\(2\)

Trace form

23 * q + 3 * q^2 + 4 * q^3 + 25 * q^4 + q^5 - 4 * q^6 + 8 * q^7 + 3 * q^8 + 31 * q^9 - 3 * q^10 + 4 * q^11 - 4 * q^12 + 14 * q^13 - 8 * q^14 - 4 * q^15 + 33 * q^16 + 8 * q^17 - 9 * q^18 + 6 * q^19 - q^20 + 32 * q^22 - 10 * q^23 + 4 * q^24 + 23 * q^25 - 26 * q^26 - 8 * q^27 + 36 * q^28 + 12 * q^29 + 12 * q^30 + 8 * q^31 - 21 * q^32 - 8 * q^33 - 10 * q^34 - 4 * q^35 + 29 * q^36 + 8 * q^37 - 36 * q^38 - 8 * q^39 - 15 * q^40 - 2 * q^41 - 40 * q^42 + 32 * q^43 - 16 * q^44 + 5 * q^45 - 12 * q^46 + 2 * q^47 - 68 * q^48 + 51 * q^49 + 3 * q^50 - 24 * q^51 + 10 * q^52 + 26 * q^53 - 24 * q^54 + 4 * q^55 - 72 * q^56 + 48 * q^57 - 30 * q^58 - 14 * q^59 - 28 * q^60 + 34 * q^61 - 32 * q^62 + 33 * q^64 - 10 * q^65 - 96 * q^66 - 3 * q^67 - 26 * q^68 - 40 * q^69 - 8 * q^70 - 24 * q^71 - 105 * q^72 + 36 * q^73 - 26 * q^74 + 4 * q^75 - 40 * q^76 - 40 * q^77 - 96 * q^78 + 48 * q^79 + 15 * q^80 + 39 * q^81 - 58 * q^82 - 60 * q^83 - 126 * q^84 - 10 * q^85 - 38 * q^86 - 28 * q^87 + 28 * q^88 + 24 * q^89 - 21 * q^90 + 32 * q^91 - 32 * q^92 - 36 * q^93 - 8 * q^94 + 12 * q^95 - 14 * q^96 + 26 * q^97 - q^98 + 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(335))\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	67
335.2.a.a	$335$	$2$	335.a	1.a	$1$	$1$	$1$	$2.675$	\(\Q\)	None	✓	✓	✓	✓	335.2.a.a	$1$	$1$	\(0\)	\(0\)	\(1\)	\(-2\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{4}+q^{5}-2q^{7}-3q^{9}-2q^{11}+\cdots\)
335.2.a.b	$335$	$2$	335.a	1.a	$1$	$2$	$2$	$2.675$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	335.2.a.b	$1$	$1$	\(0\)	\(0\)	\(-2\)	\(-4\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-\beta q^{3}-q^{5}-2q^{6}-2q^{7}+\cdots\)
335.2.a.c	$335$	$2$	335.a	1.a	$1$	$2$	$2$	$2.675$	\(\Q(\sqrt{5}) \)	None	✓	✓			335.2.a.c	$1$	$0$	\(1\)	\(0\)	\(-2\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
335.2.a.d	$335$	$2$	335.a	1.a	$1$	$7$	$7$	$2.675$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓		335.2.a.d	$1$	$0$	\(2\)	\(4\)	\(-7\)	\(10\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(\beta _{2}+\beta _{5})q^{2}+(1-\beta _{4})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
335.2.a.e	$335$	$2$	335.a	1.a	$1$	$11$	$11$	$2.675$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	335.2.a.e	$1$	$0$	\(0\)	\(0\)	\(11\)	\(4\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(335))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(335)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 2}\)