Properties

Label 1080.2.a
Level $1080$
Weight $2$
Character orbit 1080.a
Rep. character $\chi_{1080}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $14$
Sturm bound $432$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(432\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1080))\).

Total New Old
Modular forms 240 16 224
Cusp forms 193 16 177
Eisenstein series 47 0 47

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
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(10\)

Trace form

\( 16 q - 4 q^{7} + O(q^{10}) \) \( 16 q - 4 q^{7} - 4 q^{13} - 4 q^{19} + 16 q^{25} + 36 q^{31} + 4 q^{37} + 40 q^{43} + 20 q^{49} + 4 q^{55} + 4 q^{61} + 4 q^{67} + 4 q^{73} + 8 q^{79} + 4 q^{91} + 12 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1080))\) 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
1080.2.a.a 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}+2q^{11}+4q^{13}+q^{17}+\cdots\)
1080.2.a.b 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-6q^{13}+7q^{17}+7q^{19}+\cdots\)
1080.2.a.c 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{11}-5q^{13}+4q^{17}+\cdots\)
1080.2.a.d 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{11}-3q^{17}-q^{19}-3q^{23}+\cdots\)
1080.2.a.e 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-4q^{11}-2q^{13}-5q^{17}+\cdots\)
1080.2.a.f 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-q^{11}+q^{13}+q^{17}+\cdots\)
1080.2.a.g 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-2q^{11}+4q^{13}-q^{17}+\cdots\)
1080.2.a.h 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-6q^{13}-7q^{17}+7q^{19}+\cdots\)
1080.2.a.i 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}-5q^{13}-4q^{17}+\cdots\)
1080.2.a.j 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{11}+3q^{17}-q^{19}+3q^{23}+\cdots\)
1080.2.a.k 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots\)
1080.2.a.l 1080.a 1.a $1$ $8.624$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+4q^{11}-2q^{13}+5q^{17}+\cdots\)
1080.2.a.m 1080.a 1.a $2$ $8.624$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots\)
1080.2.a.n 1080.a 1.a $2$ $8.624$ \(\Q(\sqrt{73}) \) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1080))\) into lower level spaces

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