Space of modular forms of level 1480, weight 2, and trivial character

• Label: 1480.2.a
• Level: $1480$
• Weight: $2$
• Character orbit: 1480.a
• Rep. character: $\chi_{1480}(1,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $11$
• Sturm bound: $456$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1480.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(456\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1480))\).

	Total	New	Old
Modular forms	236	36	200
Cusp forms	221	36	185
Eisenstein series	15	0	15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(5\)	\(37\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(+\)	\(-\)	\(-\)	\(6\)
\(+\)	\(-\)	\(+\)	\(-\)	\(6\)
\(+\)	\(-\)	\(-\)	\(+\)	\(2\)
\(-\)	\(+\)	\(+\)	\(-\)	\(5\)
\(-\)	\(+\)	\(-\)	\(+\)	\(5\)
\(-\)	\(-\)	\(+\)	\(+\)	\(5\)
\(-\)	\(-\)	\(-\)	\(-\)	\(4\)
Plus space			\(+\)	\(15\)
Minus space			\(-\)	\(21\)

Trace form

36 * q - 4 * q^3 - 2 * q^5 + 44 * q^9 - 4 * q^11 - 4 * q^13 - 4 * q^17 - 12 * q^19 - 8 * q^21 - 8 * q^23 + 36 * q^25 - 16 * q^27 + 4 * q^29 - 8 * q^31 + 8 * q^33 + 12 * q^35 - 2 * q^37 + 24 * q^39 + 4 * q^41 - 16 * q^43 + 6 * q^45 + 16 * q^47 + 16 * q^49 + 4 * q^53 + 16 * q^57 + 20 * q^59 - 4 * q^61 - 28 * q^67 + 56 * q^69 + 16 * q^71 + 16 * q^73 - 4 * q^75 + 64 * q^77 + 24 * q^79 + 68 * q^81 - 20 * q^83 + 48 * q^89 - 32 * q^91 + 24 * q^93 + 36 * q^97 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\) 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	5	37
1480.2.a.a	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	\(\Q\)	None	✓	✓			1480.2.a.a	$1$	$2$	\(0\)	\(-3\)	\(-1\)	\(-5\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3q^{3}-q^{5}-5q^{7}+6q^{9}-3q^{11}+\cdots\)
1480.2.a.b	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	\(\Q\)	None	✓	✓			1480.2.a.b	$1$	$1$	\(0\)	\(-2\)	\(1\)	\(2\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{3}+q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
1480.2.a.c	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	\(\Q\)	None	✓	✓			1480.2.a.c	$1$	$1$	\(0\)	\(1\)	\(1\)	\(-1\)		$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}+q^{15}+\cdots\)
1480.2.a.d	$1480$	$2$	1480.a	1.a	$1$	$1$	$1$	$11.818$	\(\Q\)	None	✓	✓			1480.2.a.d	$1$	$0$	\(0\)	\(2\)	\(1\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
1480.2.a.e	$1480$	$2$	1480.a	1.a	$1$	$3$	$3$	$11.818$	3.3.316.1	None	✓	✓	✓	✓	1480.2.a.e	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-1\)		$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-q^{5}-\beta _{1}q^{7}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1480.2.a.f	$1480$	$2$	1480.a	1.a	$1$	$3$	$3$	$11.818$	3.3.568.1	None	✓	✓	✓		1480.2.a.f	$1$	$0$	\(0\)	\(1\)	\(3\)	\(-1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}-\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
1480.2.a.g	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.583504.1	None	✓	✓	✓	✓	1480.2.a.g	$1$	$1$	\(0\)	\(-5\)	\(5\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
1480.2.a.h	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.935504.1	None	✓	✓	✓	✓	1480.2.a.h	$1$	$1$	\(0\)	\(-1\)	\(-5\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
1480.2.a.i	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.6397264.1	None	✓	✓	✓		1480.2.a.i	$1$	$0$	\(0\)	\(0\)	\(-5\)	\(3\)		$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
1480.2.a.j	$1480$	$2$	1480.a	1.a	$1$	$5$	$5$	$11.818$	5.5.998068.1	None	✓	✓	✓	✓	1480.2.a.j	$1$	$0$	\(0\)	\(1\)	\(-5\)	\(-2\)		$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{4}q^{3}-q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
1480.2.a.k	$1480$	$2$	1480.a	1.a	$1$	$6$	$6$	$11.818$	6.6.693982032.1	None	✓	✓	✓	✓	1480.2.a.k	$1$	$0$	\(0\)	\(1\)	\(6\)	\(8\)		$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1480)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 2}\)