Space of modular forms of level 895, weight 2, and trivial character

• Label: 895.2.a
• Level: $895$
• Weight: $2$
• Character orbit: 895.a
• Rep. character: $\chi_{895}(1,\cdot)$
• Character field: $\Q$
• Dimension: $59$
• Newform subspaces: $7$
• Sturm bound: $180$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 895 = 5 \cdot 179 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	895.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(180\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(895))\).

	Total	New	Old
Modular forms	92	59	33
Cusp forms	89	59	30
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.

\(5\)	\(179\)	Fricke		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(14\)	\(11\)	\(3\)		\(14\)	\(11\)	\(3\)		\(0\)	\(0\)	\(0\)
\(+\)	\(-\)	\(-\)		\(32\)	\(19\)	\(13\)		\(31\)	\(19\)	\(12\)		\(1\)	\(0\)	\(1\)
\(-\)	\(+\)	\(-\)		\(22\)	\(18\)	\(4\)		\(21\)	\(18\)	\(3\)		\(1\)	\(0\)	\(1\)
\(-\)	\(-\)	\(+\)		\(24\)	\(11\)	\(13\)		\(23\)	\(11\)	\(12\)		\(1\)	\(0\)	\(1\)
Plus space		\(+\)		\(38\)	\(22\)	\(16\)		\(37\)	\(22\)	\(15\)		\(1\)	\(0\)	\(1\)
Minus space		\(-\)		\(54\)	\(37\)	\(17\)		\(52\)	\(37\)	\(15\)		\(2\)	\(0\)	\(2\)

Trace form

59 * q + 3 * q^2 + 57 * q^4 - q^5 + 4 * q^6 - 4 * q^7 + 15 * q^8 + 63 * q^9 - q^10 + 8 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 + 65 * q^16 - 6 * q^17 + 3 * q^18 - 4 * q^19 + q^20 - 28 * q^21 - 4 * q^23 - 24 * q^24 + 59 * q^25 + 2 * q^26 - 8 * q^28 - 6 * q^29 - 8 * q^30 - 12 * q^31 + 43 * q^32 + 8 * q^33 + 10 * q^34 + 8 * q^35 + 85 * q^36 + 6 * q^37 + 44 * q^38 + 20 * q^39 - 9 * q^40 + 14 * q^41 + 28 * q^42 - 12 * q^43 + 52 * q^44 - 13 * q^45 - 8 * q^46 - 12 * q^47 + 24 * q^48 + 43 * q^49 + 3 * q^50 - 20 * q^51 - 42 * q^52 + 10 * q^53 + 24 * q^54 + 4 * q^55 + 16 * q^56 + 18 * q^58 + 8 * q^59 - 12 * q^60 - 50 * q^61 + 64 * q^62 - 12 * q^63 + 45 * q^64 + 2 * q^65 - 4 * q^66 + 2 * q^68 - 56 * q^69 - 16 * q^70 + 36 * q^71 + 51 * q^72 - 2 * q^73 - 34 * q^74 - 64 * q^76 - 32 * q^77 + 8 * q^79 - 15 * q^80 + 35 * q^81 + 38 * q^82 - 44 * q^83 - 116 * q^84 - 2 * q^85 + 4 * q^86 - 16 * q^87 + 24 * q^88 + 2 * q^89 - 29 * q^90 - 40 * q^91 - 52 * q^92 - 64 * q^93 - 8 * q^94 - 12 * q^95 - 112 * q^96 - 22 * q^97 + 35 * q^98 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(895))\) 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	179
895.2.a.a	$895$	$2$	895.a	1.a	$1$	$1$	$1$	$7.147$	\(\Q\)	None	✓	✓			895.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(-1\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
895.2.a.b	$895$	$2$	895.a	1.a	$1$	$1$	$1$	$7.147$	\(\Q\)	None	✓	✓			895.2.a.b	$1$	$0$	\(-1\)	\(3\)	\(-1\)	\(-4\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+3q^{3}-q^{4}-q^{5}-3q^{6}-4q^{7}+\cdots\)
895.2.a.c	$895$	$2$	895.a	1.a	$1$	$2$	$2$	$7.147$	\(\Q(\sqrt{2}) \)	None	✓	✓			895.2.a.c	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(0\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
895.2.a.d	$895$	$2$	895.a	1.a	$1$	$8$	$8$	$7.147$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None	✓	✓	✓		895.2.a.d	$1$	$1$	\(-1\)	\(-3\)	\(-8\)	\(-2\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
895.2.a.e	$895$	$2$	895.a	1.a	$1$	$11$	$11$	$7.147$	\(\mathbb{Q}[x]/(x^{11} - \cdots)\)	None	✓	✓	✓	✓	895.2.a.e	$1$	$1$	\(-6\)	\(-4\)	\(11\)	\(-10\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}-\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
895.2.a.f	$895$	$2$	895.a	1.a	$1$	$18$	$18$	$7.147$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓		895.2.a.f	$1$	$0$	\(7\)	\(-3\)	\(-18\)	\(0\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
895.2.a.g	$895$	$2$	895.a	1.a	$1$	$18$	$18$	$7.147$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	✓	✓	✓	895.2.a.g	$1$	$0$	\(7\)	\(4\)	\(18\)	\(12\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(895))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(895)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(179))\)\(^{\oplus 2}\)