Space of modular forms of level 465, weight 2, and trivial character

• Label: 465.2.a
• Level: $465$
• Weight: $2$
• Character orbit: 465.a
• Rep. character: $\chi_{465}(1,\cdot)$
• Character field: $\Q$
• Dimension: $19$
• Newform subspaces: $8$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(465))\).

	Total	New	Old
Modular forms	68	19	49
Cusp forms	61	19	42
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.

\(3\)	\(5\)	\(31\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(+\)	\(-\)	\(-\)	\(3\)
\(+\)	\(-\)	\(+\)	\(-\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(1\)
\(-\)	\(+\)	\(+\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(+\)	\(2\)
\(-\)	\(-\)	\(+\)	\(+\)	\(1\)
\(-\)	\(-\)	\(-\)	\(-\)	\(3\)
Plus space			\(+\)	\(6\)
Minus space			\(-\)	\(13\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(465))\) 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	31
465.2.a.a	$465$	$2$	465.a	1.a	$1$	$1$	$1$	$3.713$	\(\Q\)	None	✓	✓	✓	✓	465.2.a.a	$1$	$1$	\(-1\)	\(1\)	\(1\)	\(-4\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
465.2.a.b	$465$	$2$	465.a	1.a	$1$	$1$	$1$	$3.713$	\(\Q\)	None	✓	✓	✓	✓	465.2.a.b	$1$	$1$	\(1\)	\(-1\)	\(1\)	\(-2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{2}-q^{3}-q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
465.2.a.c	$465$	$2$	465.a	1.a	$1$	$2$	$2$	$3.713$	\(\Q(\sqrt{2}) \)	None	✓	✓	✓	✓	465.2.a.c	$1$	$1$	\(-2\)	\(2\)	\(-2\)	\(-4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
465.2.a.d	$465$	$2$	465.a	1.a	$1$	$2$	$2$	$3.713$	\(\Q(\sqrt{3}) \)	None	✓	✓	✓	✓	465.2.a.d	$1$	$1$	\(0\)	\(-2\)	\(-2\)	\(-6\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{2}-q^{3}+q^{4}-q^{5}-\beta q^{6}+(-3+\cdots)q^{7}+\cdots\)
465.2.a.e	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.564.1	None	✓	✓	✓	✓	465.2.a.e	$1$	$0$	\(1\)	\(-3\)	\(-3\)	\(8\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
465.2.a.f	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.148.1	None	✓	✓	✓	✓	465.2.a.f	$1$	$0$	\(1\)	\(3\)	\(3\)	\(2\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
465.2.a.g	$465$	$2$	465.a	1.a	$1$	$3$	$3$	$3.713$	3.3.148.1	None	✓	✓	✓	✓	465.2.a.g	$1$	$0$	\(3\)	\(3\)	\(-3\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(1+\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
465.2.a.h	$465$	$2$	465.a	1.a	$1$	$4$	$4$	$3.713$	4.4.8468.1	None	✓	✓	✓	✓	465.2.a.h	$1$	$0$	\(2\)	\(-4\)	\(4\)	\(4\)		$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{1})q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(465))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(465)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(155))\)\(^{\oplus 2}\)