Properties

Label 1134.2.h
Level $1134$
Weight $2$
Character orbit 1134.h
Rep. character $\chi_{1134}(109,\cdot)$
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.h (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

\( 64q - 32q^{4} + 10q^{7} + O(q^{10}) \) \( 64q - 32q^{4} + 10q^{7} - 10q^{13} - 32q^{16} + 20q^{19} + 64q^{25} + 10q^{28} - 10q^{31} - 10q^{37} - 10q^{43} + 12q^{46} + 34q^{49} + 20q^{52} + 60q^{55} + 60q^{58} + 14q^{61} + 64q^{64} + 2q^{67} + 18q^{70} - 4q^{73} + 20q^{76} - 64q^{79} - 24q^{85} + 8q^{91} - 24q^{94} - 10q^{97} + O(q^{100}) \)

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.h.a \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-6\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.h.b \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(-5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-2q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.c \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1134.2.h.d \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.e \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.f \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.g \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(6\) \(5\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(2+\cdots)q^{7}+\cdots\)
1134.2.h.h \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(8\) \(4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{5}+(3+\cdots)q^{7}+\cdots\)
1134.2.h.i \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-8\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.j \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-6\) \(-4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.k \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-6\) \(5\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.l \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
1134.2.h.m \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1134.2.h.n \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(5\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.h.o \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(-5\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+2q^{5}+(-3+\cdots)q^{7}+\cdots\)
1134.2.h.p \(2\) \(9.055\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(6\) \(-4\) \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.h.q \(4\) \(9.055\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-2\) \(0\) \(-4\) \(0\) \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{3})q^{5}+\cdots\)
1134.2.h.r \(4\) \(9.055\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(4\) \(q+(-1-\beta _{1})q^{2}+\beta _{1}q^{4}+(1+\beta _{2})q^{7}+\cdots\)
1134.2.h.s \(4\) \(9.055\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(4\) \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+(1-\beta _{2})q^{7}+\cdots\)
1134.2.h.t \(4\) \(9.055\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(0\) \(4\) \(0\) \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{3})q^{5}+\cdots\)
1134.2.h.u \(8\) \(9.055\) 8.0.454201344.7 None \(-4\) \(0\) \(-8\) \(0\) \(q+\beta _{4}q^{2}+(-1-\beta _{4})q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
1134.2.h.v \(8\) \(9.055\) 8.0.454201344.7 None \(4\) \(0\) \(8\) \(0\) \(q-\beta _{4}q^{2}+(-1-\beta _{4})q^{4}+(1+\beta _{5})q^{5}+\cdots\)

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

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