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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
1134.2.a.a \(1\) \(9.055\) \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
1134.2.a.b \(1\) \(9.055\) \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}+q^{10}+\cdots\)
1134.2.a.c \(1\) \(9.055\) \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
1134.2.a.d \(1\) \(9.055\) \(\Q\) None \(-1\) \(0\) \(3\) \(1\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+3q^{5}+q^{7}-q^{8}-3q^{10}+\cdots\)
1134.2.a.e \(1\) \(9.055\) \(\Q\) None \(1\) \(0\) \(-3\) \(1\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}-3q^{5}+q^{7}+q^{8}-3q^{10}+\cdots\)
1134.2.a.f \(1\) \(9.055\) \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1134.2.a.g \(1\) \(9.055\) \(\Q\) None \(1\) \(0\) \(1\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
1134.2.a.h \(1\) \(9.055\) \(\Q\) None \(1\) \(0\) \(3\) \(1\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+3q^{5}+q^{7}+q^{8}+3q^{10}+\cdots\)
1134.2.a.i \(2\) \(9.055\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.j \(2\) \(9.055\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+\beta q^{5}+q^{7}-q^{8}-\beta q^{10}+\cdots\)
1134.2.a.k \(2\) \(9.055\) \(\Q(\sqrt{33}) \) None \(-2\) \(0\) \(3\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+(1+\beta )q^{5}+q^{7}-q^{8}+\cdots\)
1134.2.a.l \(2\) \(9.055\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(4\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}+(2+\beta )q^{5}-q^{7}-q^{8}+\cdots\)
1134.2.a.m \(2\) \(9.055\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-4\) \(-2\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}+(-2+\beta )q^{5}-q^{7}+q^{8}+\cdots\)
1134.2.a.n \(2\) \(9.055\) \(\Q(\sqrt{33}) \) None \(2\) \(0\) \(-3\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}+q^{8}+\cdots\)
1134.2.a.o \(2\) \(9.055\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1134.2.a.p \(2\) \(9.055\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}+(1+\beta )q^{5}-q^{7}+q^{8}+\cdots\)

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

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