↑

Properties

Label 1140.2.a
Level $1140$
Weight $2$
Character orbit 1140.a
Rep. character $\chi_{1140}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $7$
Sturm bound $480$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(480\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1140))\).

Total New Old
Modular forms 252 12 240
Cusp forms 229 12 217
Eisenstein series 23 0 23

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

\(2\)\(3\)\(5\)\(19\)FrickeDim
\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(3\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
Plus space\(+\)\(2\)
Minus space\(-\)\(10\)

Trace form

\( 12 q + 12 q^{9} + O(q^{10}) \) \( 12 q + 12 q^{9} + 8 q^{11} + 8 q^{13} + 8 q^{17} + 8 q^{23} + 12 q^{25} + 8 q^{29} + 16 q^{31} + 8 q^{33} + 8 q^{35} + 8 q^{37} - 8 q^{39} + 24 q^{41} - 8 q^{43} + 8 q^{47} + 44 q^{49} + 32 q^{53} - 4 q^{57} + 24 q^{61} + 8 q^{65} + 16 q^{69} + 48 q^{71} + 16 q^{73} + 8 q^{77} + 12 q^{81} - 8 q^{83} + 16 q^{87} - 24 q^{89} - 16 q^{91} - 16 q^{93} + 8 q^{97} + 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\) 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 19
1140.2.a.a 1140.a 1.a $1$ $9.103$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+4q^{11}+q^{15}+\cdots\)
1140.2.a.b 1140.a 1.a $1$ $9.103$ \(\Q\) None \(0\) \(1\) \(-1\) \(-4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1140.2.a.c 1140.a 1.a $1$ $9.103$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
1140.2.a.d 1140.a 1.a $1$ $9.103$ \(\Q\) None \(0\) \(1\) \(-1\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+2q^{7}+q^{9}-4q^{13}-q^{15}+\cdots\)
1140.2.a.e 1140.a 1.a $2$ $9.103$ \(\Q(\sqrt{13}) \) None \(0\) \(-2\) \(-2\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
1140.2.a.f 1140.a 1.a $3$ $9.103$ 3.3.1524.1 None \(0\) \(-3\) \(3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta _{1}q^{7}+q^{9}+(-1-\beta _{2})q^{11}+\cdots\)
1140.2.a.g 1140.a 1.a $3$ $9.103$ 3.3.564.1 None \(0\) \(3\) \(3\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(1-\beta _{2})q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1140))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1140)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 2}\)