↑

Properties

Label 1144.2.a
Level $1144$
Weight $2$
Character orbit 1144.a
Rep. character $\chi_{1144}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $12$
Sturm bound $336$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1144 = 2^{3} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1144.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(336\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1144))\).

Total New Old
Modular forms 176 30 146
Cusp forms 161 30 131
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.

\(2\)\(11\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(12\)
Minus space\(-\)\(18\)

Trace form

\( 30 q - 4 q^{5} + 22 q^{9} + O(q^{10}) \) \( 30 q - 4 q^{5} + 22 q^{9} + 6 q^{11} + 12 q^{15} + 16 q^{21} + 30 q^{25} + 24 q^{29} - 4 q^{33} - 28 q^{35} - 12 q^{37} - 16 q^{41} - 16 q^{43} + 24 q^{45} + 12 q^{47} - 2 q^{49} - 12 q^{51} + 4 q^{53} + 12 q^{59} - 24 q^{61} + 72 q^{63} + 4 q^{67} + 20 q^{69} + 8 q^{71} - 8 q^{73} + 72 q^{75} - 24 q^{79} + 30 q^{81} - 48 q^{87} + 12 q^{91} - 44 q^{93} + 40 q^{95} - 32 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\) 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 11 13
1144.2.a.a 1144.a 1.a $1$ $9.135$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{11}-q^{13}+\cdots\)
1144.2.a.b 1144.a 1.a $1$ $9.135$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
1144.2.a.c 1144.a 1.a $1$ $9.135$ \(\Q\) None \(0\) \(2\) \(3\) \(1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+3q^{5}+q^{7}+q^{9}-q^{11}-q^{13}+\cdots\)
1144.2.a.d 1144.a 1.a $1$ $9.135$ \(\Q\) None \(0\) \(3\) \(3\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}-3q^{7}+6q^{9}+q^{11}+\cdots\)
1144.2.a.e 1144.a 1.a $2$ $9.135$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
1144.2.a.f 1144.a 1.a $2$ $9.135$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}-2\beta q^{5}+\beta q^{7}+(-1+\cdots)q^{9}+\cdots\)
1144.2.a.g 1144.a 1.a $2$ $9.135$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2+2\beta )q^{5}+(2-3\beta )q^{7}+\cdots\)
1144.2.a.h 1144.a 1.a $3$ $9.135$ 3.3.229.1 None \(0\) \(0\) \(-5\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
1144.2.a.i 1144.a 1.a $3$ $9.135$ 3.3.229.1 None \(0\) \(0\) \(1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
1144.2.a.j 1144.a 1.a $3$ $9.135$ 3.3.229.1 None \(0\) \(3\) \(1\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{3}+(\beta _{1}-\beta _{2})q^{5}+(2+\beta _{1}+\cdots)q^{7}+\cdots\)
1144.2.a.k 1144.a 1.a $5$ $9.135$ 5.5.7698829.1 None \(0\) \(0\) \(-4\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(1+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
1144.2.a.l 1144.a 1.a $6$ $9.135$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(-1\) \(5\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{2})q^{5}+\beta _{5}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1144))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1144)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)