Properties

Label 1089.2.a
Level $1089$
Weight $2$
Character orbit 1089.a
Rep. character $\chi_{1089}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $23$
Sturm bound $264$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1089.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(264\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1089))\).

Total New Old
Modular forms 156 50 106
Cusp forms 109 41 68
Eisenstein series 47 9 38

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

\(3\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(10\)
Plus space\(+\)\(16\)
Minus space\(-\)\(25\)

Trace form

\( 41 q - q^{2} + 41 q^{4} - 2 q^{5} + 2 q^{7} - 3 q^{8} + O(q^{10}) \) \( 41 q - q^{2} + 41 q^{4} - 2 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} + 2 q^{13} + 12 q^{14} + 41 q^{16} - 4 q^{17} + 12 q^{19} + 4 q^{20} + 18 q^{23} + 11 q^{25} + 16 q^{26} + 4 q^{28} - 6 q^{29} - 2 q^{31} + 13 q^{32} - 8 q^{34} - 10 q^{35} + 2 q^{37} - 8 q^{38} + 18 q^{40} - 10 q^{41} - 6 q^{43} - 2 q^{46} + 16 q^{47} + 13 q^{49} + 7 q^{50} - 14 q^{52} - 8 q^{53} - 20 q^{58} + 10 q^{59} - 6 q^{61} - 22 q^{62} - 7 q^{64} + 8 q^{65} - 18 q^{67} - 2 q^{68} - 16 q^{70} + 2 q^{71} + 14 q^{73} - 12 q^{76} + 34 q^{79} + 56 q^{80} - 36 q^{82} + 6 q^{83} + 14 q^{85} + 20 q^{86} + 22 q^{89} + 44 q^{91} + 12 q^{92} - 8 q^{94} + 42 q^{97} + 15 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 11
1089.2.a.a \(1\) \(8.696\) \(\Q\) None \(-2\) \(0\) \(-4\) \(-1\) \(-\) \(-\) \(q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots\)
1089.2.a.b \(1\) \(8.696\) \(\Q\) None \(-2\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots\)
1089.2.a.c \(1\) \(8.696\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-2\) \(-\) \(-\) \(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
1089.2.a.d \(1\) \(8.696\) \(\Q\) None \(-1\) \(0\) \(4\) \(2\) \(+\) \(-\) \(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
1089.2.a.e \(1\) \(8.696\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) \(+\) \(-\) \(q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots\)
1089.2.a.f \(1\) \(8.696\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) \(+\) \(-\) \(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots\)
1089.2.a.g \(1\) \(8.696\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(3\) \(0\) \(-\) \(+\) \(q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots\)
1089.2.a.h \(1\) \(8.696\) \(\Q\) None \(1\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots\)
1089.2.a.i \(1\) \(8.696\) \(\Q\) None \(1\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots\)
1089.2.a.j \(1\) \(8.696\) \(\Q\) None \(1\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots\)
1089.2.a.k \(1\) \(8.696\) \(\Q\) None \(2\) \(0\) \(-4\) \(1\) \(-\) \(-\) \(q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots\)
1089.2.a.l \(2\) \(8.696\) \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(-1\) \(2\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.m \(2\) \(8.696\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(3\) \(6\) \(-\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
1089.2.a.n \(2\) \(8.696\) \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
1089.2.a.o \(2\) \(8.696\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(6\) \(0\) \(-\) \(+\) \(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.p \(2\) \(8.696\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-4\) \(0\) \(-\) \(+\) \(q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.q \(2\) \(8.696\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.r \(2\) \(8.696\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.s \(2\) \(8.696\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(-6\) \(-\) \(-\) \(q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots\)
1089.2.a.t \(2\) \(8.696\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(-1\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.u \(4\) \(8.696\) \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(0\) \(-2\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1089.2.a.v \(4\) \(8.696\) 4.4.4400.1 None \(0\) \(0\) \(0\) \(-8\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1089.2.a.w \(4\) \(8.696\) 4.4.4400.1 None \(0\) \(0\) \(0\) \(8\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1089))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1089)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)