Properties

Label 1134.2.e
Level $1134$
Weight $2$
Character orbit 1134.e
Rep. character $\chi_{1134}(865,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $22$
Sturm bound $432$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 22 \)
Sturm bound: \(432\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1134, [\chi])\).

Total New Old
Modular forms 480 64 416
Cusp forms 384 64 320
Eisenstein series 96 0 96

Trace form

\( 64q + 64q^{4} + 10q^{7} + O(q^{10}) \) \( 64q + 64q^{4} + 10q^{7} - 10q^{13} + 64q^{16} + 20q^{19} - 32q^{25} + 10q^{28} + 20q^{31} - 10q^{37} - 10q^{43} + 12q^{46} - 2q^{49} - 10q^{52} + 60q^{55} - 30q^{58} - 28q^{61} + 64q^{64} - 4q^{67} + 54q^{70} - 4q^{73} + 20q^{76} + 128q^{79} - 24q^{85} + 8q^{91} + 48q^{94} - 10q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1134, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1134.2.e.a \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-1\) \(q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1134.2.e.b \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-2\) \(4\) \(q-q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1134.2.e.c \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-1\) \(q-q^{2}+q^{4}+(1-3\zeta_{6})q^{7}-q^{8}-6\zeta_{6}q^{11}+\cdots\)
1134.2.e.d \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(5\) \(q-q^{2}+q^{4}+(2+\zeta_{6})q^{7}-q^{8}+4\zeta_{6}q^{13}+\cdots\)
1134.2.e.e \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(-5\) \(q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.f \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(-1\) \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1134.2.e.g \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(5\) \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.e.h \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(4\) \(-5\) \(q-q^{2}+q^{4}+(4-4\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.i \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-4\) \(-5\) \(q+q^{2}+q^{4}+(-4+4\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1134.2.e.j \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(-1\) \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1134.2.e.k \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(5\) \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.e.l \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-1\) \(-5\) \(q+q^{2}+q^{4}+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.m \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(-1\) \(q+q^{2}+q^{4}+(1-3\zeta_{6})q^{7}+q^{8}+6\zeta_{6}q^{11}+\cdots\)
1134.2.e.n \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(5\) \(q+q^{2}+q^{4}+(2+\zeta_{6})q^{7}+q^{8}+4\zeta_{6}q^{13}+\cdots\)
1134.2.e.o \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(4\) \(q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1134.2.e.p \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-1\) \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1134.2.e.q \(4\) \(9.055\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-4\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1134.2.e.r \(4\) \(9.055\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(0\) \(-2\) \(q-q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1134.2.e.s \(4\) \(9.055\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(0\) \(-2\) \(q+q^{2}+q^{4}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
1134.2.e.t \(4\) \(9.055\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(4\) \(0\) \(2\) \(0\) \(q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
1134.2.e.u \(8\) \(9.055\) 8.0.454201344.7 None \(-8\) \(0\) \(-4\) \(6\) \(q-q^{2}+q^{4}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1134.2.e.v \(8\) \(9.055\) 8.0.454201344.7 None \(8\) \(0\) \(4\) \(6\) \(q+q^{2}+q^{4}+(\beta _{3}-\beta _{4}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1134, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)