Properties

Label 1134.2.f
Level $1134$
Weight $2$
Character orbit 1134.f
Rep. character $\chi_{1134}(379,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $20$
Sturm bound $432$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 20 \)
Sturm bound: \(432\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 480 48 432
Cusp forms 384 48 336
Eisenstein series 96 0 96

Trace form

\( 48 q - 24 q^{4} + O(q^{10}) \) \( 48 q - 24 q^{4} - 24 q^{16} - 24 q^{19} + 12 q^{22} + 24 q^{31} + 12 q^{34} - 48 q^{37} + 12 q^{43} - 24 q^{49} - 48 q^{55} + 48 q^{64} + 36 q^{67} - 24 q^{73} + 12 q^{76} + 24 q^{79} + 12 q^{85} + 12 q^{88} - 48 q^{91} + 24 q^{97} + O(q^{100}) \)

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.f.a 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
1134.2.f.b 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1134.2.f.c 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.d 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.e 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.f 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.g 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+2\zeta_{6}q^{5}+\cdots\)
1134.2.f.h 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1134.2.f.i 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.f.j 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-2\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.k 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.l 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+(-1+\zeta_{6})q^{7}+\cdots\)
1134.2.f.m 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1134.2.f.n 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
1134.2.f.o 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1134.2.f.p 1134.f 9.c $2$ $9.055$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1134.2.f.q 1134.f 9.c $4$ $9.055$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1134.2.f.r 1134.f 9.c $4$ $9.055$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}q^{2}+(-1+\zeta_{12})q^{4}+(2-2\zeta_{12}+\cdots)q^{5}+\cdots\)
1134.2.f.s 1134.f 9.c $4$ $9.055$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}+(-2\zeta_{12}+\cdots)q^{5}+\cdots\)
1134.2.f.t 1134.f 9.c $4$ $9.055$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{12})q^{2}-\zeta_{12}q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(162, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)