Space of modular forms of level 435, weight 2, and trivial character

• Label: 435.2.a
• Level: $435$
• Weight: $2$
• Character orbit: 435.a
• Rep. character: $\chi_{435}(1,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $10$
• Sturm bound: $120$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(120\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(435))\).

	Total	New	Old
Modular forms	64	19	45
Cusp forms	57	19	38
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.

\(3\)	\(5\)	\(29\)	Fricke		Total				Cusp				Eisenstein
					All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)		\(5\)	\(4\)	\(1\)		\(5\)	\(4\)	\(1\)		\(0\)	\(0\)	\(0\)
\(+\)	\(+\)	\(-\)	\(-\)		\(10\)	\(1\)	\(9\)		\(9\)	\(1\)	\(8\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(+\)	\(-\)		\(8\)	\(3\)	\(5\)		\(7\)	\(3\)	\(4\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)	\(+\)		\(9\)	\(0\)	\(9\)		\(8\)	\(0\)	\(8\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)		\(7\)	\(3\)	\(4\)		\(6\)	\(3\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)	\(+\)		\(8\)	\(2\)	\(6\)		\(7\)	\(2\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)	\(+\)		\(6\)	\(0\)	\(6\)		\(5\)	\(0\)	\(5\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)		\(11\)	\(6\)	\(5\)		\(10\)	\(6\)	\(4\)		\(1\)	\(0\)	\(1\)
Plus space			\(+\)		\(28\)	\(6\)	\(22\)		\(25\)	\(6\)	\(19\)		\(3\)	\(0\)	\(3\)
Minus space			\(-\)		\(36\)	\(13\)	\(23\)		\(32\)	\(13\)	\(19\)		\(4\)	\(0\)	\(4\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(435))\) 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	29
435.2.a.a	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	\(\Q\)	None	✓	✓			435.2.a.a	$1$	$0$	\(-1\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
435.2.a.b	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	\(\Q\)	None	✓	✓	✓	✓	435.2.a.b	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(-2\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
435.2.a.c	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	\(\Q\)	None	✓	✓			435.2.a.c	$1$	$0$	\(0\)	\(1\)	\(-1\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots\)
435.2.a.d	$435$	$2$	435.a	1.a	$1$	$1$	$1$	$3.473$	\(\Q\)	None	✓	✓			435.2.a.d	$1$	$0$	\(1\)	\(1\)	\(1\)	\(4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
435.2.a.e	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓	✓	435.2.a.e	$1$	$1$	\(-1\)	\(2\)	\(-2\)	\(-6\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
435.2.a.f	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	\(\Q(\sqrt{21}) \)	None	✓	✓			435.2.a.f	$1$	$0$	\(-1\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+(3+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
435.2.a.g	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	\(\Q(\sqrt{5}) \)	None	✓	✓	✓		435.2.a.g	$1$	$0$	\(0\)	\(2\)	\(-2\)	\(4\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta q^{2}+q^{3}+3q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots\)
435.2.a.h	$435$	$2$	435.a	1.a	$1$	$2$	$2$	$3.473$	\(\Q(\sqrt{17}) \)	None	✓	✓			435.2.a.h	$1$	$0$	\(1\)	\(2\)	\(2\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
435.2.a.i	$435$	$2$	435.a	1.a	$1$	$3$	$3$	$3.473$	3.3.469.1	None	✓	✓	✓	✓	435.2.a.i	$1$	$0$	\(1\)	\(-3\)	\(3\)	\(-4\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
435.2.a.j	$435$	$2$	435.a	1.a	$1$	$4$	$4$	$3.473$	\(\Q(\sqrt{38 +2 \sqrt{5}})\)	None	✓	✓	✓	✓	435.2.a.j	$1$	$1$	\(-3\)	\(-4\)	\(-4\)	\(2\)		$+$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(435))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(435)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)