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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1134.2.e.a 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1134.2.e.b 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-2+2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1134.2.e.c 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(1-3\zeta_{6})q^{7}-q^{8}-6\zeta_{6}q^{11}+\cdots\)
1134.2.e.d 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(2+\zeta_{6})q^{7}-q^{8}+4\zeta_{6}q^{13}+\cdots\)
1134.2.e.e 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(1-\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.f 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1134.2.e.g 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.e.h 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(4-4\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.i 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-4+4\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1134.2.e.j 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1134.2.e.k 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-3+3\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1134.2.e.l 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-1+\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1134.2.e.m 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(1-3\zeta_{6})q^{7}+q^{8}+6\zeta_{6}q^{11}+\cdots\)
1134.2.e.n 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(2+\zeta_{6})q^{7}+q^{8}+4\zeta_{6}q^{13}+\cdots\)
1134.2.e.o 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(2-2\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1134.2.e.p 1134.e 63.h $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(3-3\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1134.2.e.q 1134.e 63.h $4$ $9.055$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-4\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1134.2.e.r 1134.e 63.h $4$ $9.055$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1134.2.e.s 1134.e 63.h $4$ $9.055$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{7}+\cdots\)
1134.2.e.t 1134.e 63.h $4$ $9.055$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(4\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
1134.2.e.u 1134.e 63.h $8$ $9.055$ 8.0.454201344.7 None \(-8\) \(0\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
1134.2.e.v 1134.e 63.h $8$ $9.055$ 8.0.454201344.7 None \(8\) \(0\) \(4\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(\beta _{3}-\beta _{4}+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)

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

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