Properties

Label 1134.2.t
Level $1134$
Weight $2$
Character orbit 1134.t
Rep. character $\chi_{1134}(593,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $8$
Sturm bound $432$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 8 \)
Sturm bound: \(432\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\), \(11\)

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

\( 64q + 32q^{4} - 10q^{7} + O(q^{10}) \) \( 64q + 32q^{4} - 10q^{7} + 30q^{13} - 32q^{16} + 64q^{25} + 10q^{28} - 30q^{31} + 10q^{37} + 10q^{43} - 12q^{46} - 14q^{49} + 60q^{58} + 30q^{61} - 64q^{64} + 2q^{67} + 18q^{70} + 44q^{79} + 24q^{85} - 12q^{91} + 30q^{97} + O(q^{100}) \)

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.t.a \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-10\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1134.2.t.b \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1134.2.t.c \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1134.2.t.d \(4\) \(9.055\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{4}+\cdots\)
1134.2.t.e \(8\) \(9.055\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) \(q+(\zeta_{24}-\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
1134.2.t.f \(8\) \(9.055\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(4\) \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(1-\zeta_{24}^{2})q^{4}+\cdots\)
1134.2.t.g \(16\) \(9.055\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{9}q^{2}+(1+\beta _{2})q^{4}+\beta _{6}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)
1134.2.t.h \(16\) \(9.055\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{4}q^{2}-\beta _{2}q^{4}-\beta _{6}q^{5}+(\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)

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

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