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Properties

Label 1134.2.a
Level $1134$
Weight $2$
Character orbit 1134.a
Rep. character $\chi_{1134}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $16$
Sturm bound $432$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(432\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1134))\).

Total New Old
Modular forms 240 24 216
Cusp forms 193 24 169
Eisenstein series 47 0 47

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(8\)
Minus space\(-\)\(16\)

Trace form

\( 24 q + 24 q^{4} + O(q^{10}) \) \( 24 q + 24 q^{4} - 12 q^{10} - 12 q^{13} + 24 q^{16} + 12 q^{19} + 12 q^{22} + 36 q^{25} + 24 q^{31} + 12 q^{37} - 12 q^{40} + 12 q^{43} + 24 q^{49} - 12 q^{52} + 24 q^{55} - 12 q^{58} - 12 q^{61} + 24 q^{64} + 36 q^{67} + 12 q^{76} + 24 q^{79} - 12 q^{82} - 12 q^{85} + 12 q^{88} + 24 q^{91} - 36 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1134))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
1134.2.a.a 1134.a 1.a $1$ $9.055$ \(\Q\) None 126.2.f.a \(-1\) \(0\) \(-3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1134.2.a.b 1134.a 1.a $1$ $9.055$ \(\Q\) None 1134.2.a.b \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1134.2.a.c 1134.a 1.a $1$ $9.055$ \(\Q\) None 126.2.f.b \(-1\) \(0\) \(2\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
1134.2.a.d 1134.a 1.a $1$ $9.055$ \(\Q\) None 1134.2.a.d \(-1\) \(0\) \(3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1134.2.a.e 1134.a 1.a $1$ $9.055$ \(\Q\) None 1134.2.a.d \(1\) \(0\) \(-3\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1134.2.a.f 1134.a 1.a $1$ $9.055$ \(\Q\) None 126.2.f.b \(1\) \(0\) \(-2\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1134.2.a.g 1134.a 1.a $1$ $9.055$ \(\Q\) None 1134.2.a.b \(1\) \(0\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1134.2.a.h 1134.a 1.a $1$ $9.055$ \(\Q\) None 126.2.f.a \(1\) \(0\) \(3\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1134.2.a.i 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{6}) \) None 126.2.f.c \(-2\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.j 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{3}) \) None 1134.2.a.j \(-2\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1134.2.a.k 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{33}) \) None 126.2.f.d \(-2\) \(0\) \(3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
1134.2.a.l 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{3}) \) None 1134.2.a.l \(-2\) \(0\) \(4\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.m 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{3}) \) None 1134.2.a.l \(2\) \(0\) \(-4\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
1134.2.a.n 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{33}) \) None 126.2.f.d \(2\) \(0\) \(-3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}+q^{8}+\cdots\)
1134.2.a.o 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{3}) \) None 1134.2.a.j \(2\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1134.2.a.p 1134.a 1.a $2$ $9.055$ \(\Q(\sqrt{6}) \) None 126.2.f.c \(2\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1134))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1134)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(81))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(162))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(567))\)\(^{\oplus 2}\)