Properties

Label 1053.2.e
Level $1053$
Weight $2$
Character orbit 1053.e
Rep. character $\chi_{1053}(352,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $19$
Sturm bound $252$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1053.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 19 \)
Sturm bound: \(252\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1053, [\chi])\).

Total New Old
Modular forms 276 96 180
Cusp forms 228 96 132
Eisenstein series 48 0 48

Trace form

\( 96 q - 48 q^{4} + O(q^{10}) \) \( 96 q - 48 q^{4} - 48 q^{16} + 24 q^{19} - 12 q^{22} - 60 q^{25} - 12 q^{31} + 48 q^{34} + 24 q^{37} + 60 q^{40} - 12 q^{43} - 72 q^{46} - 72 q^{49} - 96 q^{55} + 60 q^{58} - 24 q^{61} - 24 q^{64} - 24 q^{67} + 36 q^{70} + 72 q^{73} + 24 q^{76} + 60 q^{79} + 24 q^{82} + 24 q^{88} + 36 q^{94} - 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1053, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1053.2.e.a 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1053.2.e.b 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
1053.2.e.c 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(-5+\cdots)q^{7}+\cdots\)
1053.2.e.d 1053.e 9.c $2$ $8.408$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+2\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
1053.2.e.e 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1053.2.e.f 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(-1\) \(0\) \(-5\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1053.2.e.g 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1053.2.e.h 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1053.2.e.i 1053.e 9.c $4$ $8.408$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(-1+\zeta_{12})q^{4}-2\zeta_{12}q^{7}+\cdots\)
1053.2.e.j 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(0\) \(5\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
1053.2.e.k 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(0\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.e.l 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.e.m 1053.e 9.c $4$ $8.408$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)
1053.2.e.n 1053.e 9.c $6$ $8.408$ 6.0.1156923.1 None \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
1053.2.e.o 1053.e 9.c $6$ $8.408$ 6.0.1156923.1 None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-\beta _{1}+\beta _{2}-2\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
1053.2.e.p 1053.e 9.c $8$ $8.408$ 8.0.4678560000.4 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-2-2\beta _{3}-\beta _{4})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1053.2.e.q 1053.e 9.c $8$ $8.408$ 8.0.\(\cdots\).8 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{7}q^{2}+(-1+\beta _{2}-\beta _{4})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
1053.2.e.r 1053.e 9.c $8$ $8.408$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+\beta _{4}q^{4}+\beta _{2}q^{5}+(2+\beta _{4}+\cdots)q^{7}+\cdots\)
1053.2.e.s 1053.e 9.c $16$ $8.408$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{13}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{4}-2\beta _{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1053, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1053, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(81, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)