Properties

Label 1152.2.a
Level $1152$
Weight $2$
Character orbit 1152.a
Rep. character $\chi_{1152}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $20$
Sturm bound $384$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(384\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1152))\).

Total New Old
Modular forms 224 20 204
Cusp forms 161 20 141
Eisenstein series 63 0 63

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

\(2\)\(3\)FrickeDim.
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(5\)
Plus space\(+\)\(9\)
Minus space\(-\)\(11\)

Trace form

\( 20q + O(q^{10}) \) \( 20q - 8q^{17} + 12q^{25} + 8q^{41} - 12q^{49} + 16q^{65} - 8q^{73} + 56q^{89} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1152))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
1152.2.a.a \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) \(+\) \(-\) \(q-4q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.b \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-4\) \(2\) \(-\) \(-\) \(q-4q^{5}+2q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.c \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) \(+\) \(-\) \(q-2q^{5}-4q^{7}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.d \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(q-2q^{5}-2q^{7}+4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.e \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) \(+\) \(+\) \(q-2q^{5}-2q^{7}+4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.f \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(q-2q^{5}+2q^{7}-4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.g \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(2\) \(+\) \(+\) \(q-2q^{5}+2q^{7}-4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.h \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(-2\) \(4\) \(+\) \(-\) \(q-2q^{5}+4q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.i \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(q-2q^{7}-4q^{11}+6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.j \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(q-2q^{7}+4q^{11}-6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.k \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+2q^{7}-4q^{11}-6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.l \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(+\) \(-\) \(q+2q^{7}+4q^{11}+6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.m \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(-4\) \(-\) \(-\) \(q+2q^{5}-4q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.n \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(+\) \(+\) \(q+2q^{5}-2q^{7}-4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.o \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(q+2q^{5}-2q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.p \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q+2q^{5}+2q^{7}+4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.q \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q+2q^{5}+2q^{7}+4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.r \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(2\) \(4\) \(+\) \(-\) \(q+2q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.s \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(4\) \(-2\) \(+\) \(-\) \(q+4q^{5}-2q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.t \(1\) \(9.199\) \(\Q\) None \(0\) \(0\) \(4\) \(2\) \(+\) \(-\) \(q+4q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1152))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1152)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(576))\)\(^{\oplus 2}\)