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Properties

Label 1134.2.d
Level $1134$
Weight $2$
Character orbit 1134.d
Rep. character $\chi_{1134}(1133,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $2$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(432\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 240 32 208
Cusp forms 192 32 160
Eisenstein series 48 0 48

Trace form

\( 32 q - 32 q^{4} + 4 q^{7} + O(q^{10}) \) \( 32 q - 32 q^{4} + 4 q^{7} + 32 q^{16} + 32 q^{25} - 4 q^{28} + 8 q^{37} + 56 q^{43} + 24 q^{46} - 16 q^{49} - 24 q^{58} - 32 q^{64} + 40 q^{67} - 24 q^{70} + 40 q^{79} - 24 q^{85} + 48 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.d.a 1134.d 21.c $16$ $9.055$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+\beta _{2}q^{5}-\beta _{8}q^{7}-\beta _{1}q^{8}+\cdots\)
1134.2.d.b 1134.d 21.c $16$ $9.055$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{2}-q^{4}-\beta _{2}q^{5}+\beta _{14}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1134, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)