Properties

Label 1080.4.a
Level $1080$
Weight $4$
Character orbit 1080.a
Rep. character $\chi_{1080}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $16$
Sturm bound $864$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(864\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1080))\).

Total New Old
Modular forms 672 48 624
Cusp forms 624 48 576
Eisenstein series 48 0 48

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(7\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(6\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(7\)
\(-\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(26\)
Minus space\(-\)\(22\)

Trace form

\( 48 q - 36 q^{7} + O(q^{10}) \) \( 48 q - 36 q^{7} + 36 q^{13} - 180 q^{19} + 1200 q^{25} - 588 q^{31} - 420 q^{37} + 360 q^{43} + 2652 q^{49} + 180 q^{55} - 900 q^{61} - 492 q^{67} - 180 q^{73} + 120 q^{79} + 9012 q^{91} + 228 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1080))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5
1080.4.a.a 1080.a 1.a $2$ $63.722$ \(\Q(\sqrt{241}) \) None \(0\) \(0\) \(-10\) \(-5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(-2-\beta )q^{7}+(3-\beta )q^{11}+\cdots\)
1080.4.a.b 1080.a 1.a $2$ $63.722$ \(\Q(\sqrt{241}) \) None \(0\) \(0\) \(10\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(-2-\beta )q^{7}+(-3+\beta )q^{11}+\cdots\)
1080.4.a.c 1080.a 1.a $3$ $63.722$ 3.3.697.1 None \(0\) \(0\) \(-15\) \(-24\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(-8-\beta _{2})q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots\)
1080.4.a.d 1080.a 1.a $3$ $63.722$ 3.3.1257.1 None \(0\) \(0\) \(-15\) \(-10\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(-4+\beta _{1}+\beta _{2})q^{7}+(-11+\cdots)q^{11}+\cdots\)
1080.4.a.e 1080.a 1.a $3$ $63.722$ 3.3.4281.1 None \(0\) \(0\) \(-15\) \(-8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(-3+\beta _{1})q^{7}+(4-\beta _{1}+\beta _{2})q^{11}+\cdots\)
1080.4.a.f 1080.a 1.a $3$ $63.722$ 3.3.1765.1 None \(0\) \(0\) \(-15\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}-\beta _{1}q^{7}+(9+\beta _{1}-2\beta _{2})q^{11}+\cdots\)
1080.4.a.g 1080.a 1.a $3$ $63.722$ 3.3.985.1 None \(0\) \(0\) \(-15\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(2-\beta _{2})q^{7}+(-4+\beta _{1}+\beta _{2})q^{11}+\cdots\)
1080.4.a.h 1080.a 1.a $3$ $63.722$ 3.3.47977.1 None \(0\) \(0\) \(-15\) \(9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(3+\beta _{2})q^{7}+(-6-\beta _{1}+\beta _{2})q^{11}+\cdots\)
1080.4.a.i 1080.a 1.a $3$ $63.722$ 3.3.697.1 None \(0\) \(0\) \(15\) \(-24\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(-8-\beta _{2})q^{7}+(2-\beta _{1}+3\beta _{2})q^{11}+\cdots\)
1080.4.a.j 1080.a 1.a $3$ $63.722$ 3.3.1257.1 None \(0\) \(0\) \(15\) \(-10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(-4+\beta _{1}+\beta _{2})q^{7}+(11-5\beta _{1}+\cdots)q^{11}+\cdots\)
1080.4.a.k 1080.a 1.a $3$ $63.722$ 3.3.4281.1 None \(0\) \(0\) \(15\) \(-8\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(-3+\beta _{1})q^{7}+(-4+\beta _{1}+\cdots)q^{11}+\cdots\)
1080.4.a.l 1080.a 1.a $3$ $63.722$ 3.3.1765.1 None \(0\) \(0\) \(15\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}-\beta _{1}q^{7}+(-9-\beta _{1}+2\beta _{2})q^{11}+\cdots\)
1080.4.a.m 1080.a 1.a $3$ $63.722$ 3.3.985.1 None \(0\) \(0\) \(15\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(2-\beta _{2})q^{7}+(4-\beta _{1}-\beta _{2})q^{11}+\cdots\)
1080.4.a.n 1080.a 1.a $3$ $63.722$ 3.3.47977.1 None \(0\) \(0\) \(15\) \(9\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(3+\beta _{2})q^{7}+(6+\beta _{1}-\beta _{2})q^{11}+\cdots\)
1080.4.a.o 1080.a 1.a $4$ $63.722$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(-20\) \(14\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-5q^{5}+(3-\beta _{2})q^{7}+(1-\beta _{1})q^{11}+\cdots\)
1080.4.a.p 1080.a 1.a $4$ $63.722$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(0\) \(20\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+5q^{5}+(3-\beta _{2})q^{7}+(-1+\beta _{1})q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1080))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1080)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(540))\)\(^{\oplus 2}\)