↑

Properties

Label 1122.2.a
Level $1122$
Weight $2$
Character orbit 1122.a
Rep. character $\chi_{1122}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $19$
Sturm bound $432$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1122.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(13\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1122))\).

Total New Old
Modular forms 224 25 199
Cusp forms 209 25 184
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.

\(2\)\(3\)\(11\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(+\)\(-\)$-$\(2\)
\(+\)\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(+\)\(-\)\(-\)$+$\(2\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(1\)
\(+\)\(-\)\(-\)\(-\)$-$\(2\)
\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(2\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(3\)
Plus space\(+\)\(9\)
Minus space\(-\)\(16\)

Trace form

\( 25 q + q^{2} - 3 q^{3} + 25 q^{4} + 6 q^{5} + q^{6} + q^{8} + 25 q^{9} + O(q^{10}) \) \( 25 q + q^{2} - 3 q^{3} + 25 q^{4} + 6 q^{5} + q^{6} + q^{8} + 25 q^{9} + 6 q^{10} + q^{11} - 3 q^{12} + 6 q^{13} + 8 q^{14} + 6 q^{15} + 25 q^{16} + q^{17} + q^{18} - 4 q^{19} + 6 q^{20} - 16 q^{21} - 3 q^{22} - 16 q^{23} + q^{24} + 7 q^{25} + 6 q^{26} - 3 q^{27} - 2 q^{29} + 6 q^{30} + q^{32} + q^{33} - 7 q^{34} + 25 q^{36} + 6 q^{37} - 20 q^{38} - 26 q^{39} + 6 q^{40} + 10 q^{41} + 8 q^{42} - 44 q^{43} + q^{44} + 6 q^{45} + 8 q^{46} + 16 q^{47} - 3 q^{48} + 33 q^{49} + 15 q^{50} + q^{51} + 6 q^{52} - 18 q^{53} + q^{54} + 6 q^{55} + 8 q^{56} - 4 q^{57} + 14 q^{58} - 12 q^{59} + 6 q^{60} - 10 q^{61} + 25 q^{64} + 20 q^{65} + q^{66} + 4 q^{67} + q^{68} + 8 q^{69} + 32 q^{70} + 16 q^{71} + q^{72} + 34 q^{73} + 22 q^{74} + 3 q^{75} - 4 q^{76} + 6 q^{78} - 56 q^{79} + 6 q^{80} + 25 q^{81} + 10 q^{82} + 4 q^{83} - 16 q^{84} + 6 q^{85} - 12 q^{86} - 2 q^{87} - 3 q^{88} + 42 q^{89} + 6 q^{90} + 16 q^{91} - 16 q^{92} + 8 q^{93} + 16 q^{94} + 8 q^{95} + q^{96} - 14 q^{97} - 23 q^{98} + q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\) 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 11 17
1122.2.a.a 1122.a 1.a $1$ $8.959$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1122.2.a.b 1122.a 1.a $1$ $8.959$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.c 1122.a 1.a $1$ $8.959$ \(\Q\) None \(-1\) \(-1\) \(2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.d 1122.a 1.a $1$ $8.959$ \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.e 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.f 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.g 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(-1\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.h 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(-1\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
1122.2.a.i 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
1122.2.a.j 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.k 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.l 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.m 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(2\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.n 1122.a 1.a $1$ $8.959$ \(\Q\) None \(1\) \(1\) \(4\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.o 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(-2\) \(6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1122.2.a.p 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1122.2.a.q 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1122.2.a.r 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1122.2.a.s 1122.a 1.a $3$ $8.959$ 3.3.148.1 None \(3\) \(-3\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1122))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1122)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(374))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(561))\)\(^{\oplus 2}\)