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 $13$

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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

\( 25 q + q^{2} - 3 q^{3} + 25 q^{4} + 6 q^{5} + q^{6} + q^{8} + 25 q^{9} + 6 q^{10} + q^{11} - 3 q^{12} + 6 q^{13} + 8 q^{14} + 6 q^{15} + 25 q^{16} + q^{17} + q^{18} - 4 q^{19} + 6 q^{20} - 16 q^{21}+ \cdots + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1122))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist 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 1122.2.a.a \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
1122.2.a.b 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.b \(-1\) \(-1\) \(2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.c 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.c \(-1\) \(-1\) \(2\) \(4\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.d 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.d \(-1\) \(1\) \(-2\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.e 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.e \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.f 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.f \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
1122.2.a.g 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.g \(1\) \(-1\) \(2\) \(-2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
1122.2.a.h 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.h \(1\) \(-1\) \(2\) \(4\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+4q^{7}+\cdots\)
1122.2.a.i 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.i \(1\) \(1\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
1122.2.a.j 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.j \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.k 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.k \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
1122.2.a.l 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.l \(1\) \(1\) \(2\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.m 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.m \(1\) \(1\) \(2\) \(4\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+4q^{7}+\cdots\)
1122.2.a.n 1122.a 1.a $1$ $8.959$ \(\Q\) None 1122.2.a.n \(1\) \(1\) \(4\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-2q^{7}+\cdots\)
1122.2.a.o 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None 1122.2.a.o \(-2\) \(-2\) \(-2\) \(6\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1122.2.a.p 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None 1122.2.a.p \(-2\) \(-2\) \(0\) \(-4\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2+\beta )q^{7}+\cdots\)
1122.2.a.q 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{2}) \) None 1122.2.a.q \(-2\) \(2\) \(0\) \(-4\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots\)
1122.2.a.r 1122.a 1.a $2$ $8.959$ \(\Q(\sqrt{5}) \) None 1122.2.a.r \(-2\) \(2\) \(2\) \(-2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1122.2.a.s 1122.a 1.a $3$ $8.959$ 3.3.148.1 None 1122.2.a.s \(3\) \(-3\) \(0\) \(2\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)

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

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