Properties

Label 1089.3.b
Level $1089$
Weight $3$
Character orbit 1089.b
Rep. character $\chi_{1089}(485,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $10$
Sturm bound $396$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1089 = 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1089.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(396\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1089, [\chi])\).

Total New Old
Modular forms 288 72 216
Cusp forms 240 72 168
Eisenstein series 48 0 48

Trace form

\( 72q - 144q^{4} - 16q^{7} + O(q^{10}) \) \( 72q - 144q^{4} - 16q^{7} + 48q^{10} + 8q^{13} + 216q^{16} - 40q^{19} - 288q^{25} + 32q^{28} + 56q^{31} + 200q^{34} - 104q^{37} - 432q^{40} + 104q^{43} - 24q^{46} + 592q^{49} - 280q^{52} + 536q^{58} + 8q^{61} - 168q^{64} - 144q^{67} + 64q^{70} - 448q^{73} + 344q^{76} - 448q^{79} - 744q^{82} - 48q^{85} + 632q^{91} - 360q^{94} + 640q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1089, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1089.3.b.a \(2\) \(29.673\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta q^{2}+2q^{4}-4\beta q^{5}-q^{7}+6\beta q^{8}+\cdots\)
1089.3.b.b \(2\) \(29.673\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{2}+2q^{4}+4\beta q^{5}+q^{7}+6\beta q^{8}+\cdots\)
1089.3.b.c \(4\) \(29.673\) \(\Q(\sqrt{-2}, \sqrt{15})\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{1}q^{2}+(-4+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.d \(4\) \(29.673\) \(\Q(\sqrt{-2}, \sqrt{15})\) None \(0\) \(0\) \(0\) \(20\) \(q+\beta _{1}q^{2}+(-4+\beta _{3})q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.e \(4\) \(29.673\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}-2q^{4}+2\beta _{3}q^{5}-7\beta _{2}q^{7}+\cdots\)
1089.3.b.f \(8\) \(29.673\) 8.0.\(\cdots\).10 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-4-\beta _{2})q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
1089.3.b.g \(8\) \(29.673\) 8.0.\(\cdots\).6 None \(0\) \(0\) \(0\) \(-16\) \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1089.3.b.h \(8\) \(29.673\) 8.0.3317760000.7 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+\beta _{3}q^{4}-\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
1089.3.b.i \(16\) \(29.673\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{13}q^{5}+\cdots\)
1089.3.b.j \(16\) \(29.673\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(8\) \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{13}q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1089, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1089, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(363, [\chi])\)\(^{\oplus 2}\)