Properties

Label 1152.3.b
Level $1152$
Weight $3$
Character orbit 1152.b
Rep. character $\chi_{1152}(703,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $10$
Sturm bound $576$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(576\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1152, [\chi])\).

Total New Old
Modular forms 416 40 376
Cusp forms 352 40 312
Eisenstein series 64 0 64

Trace form

\( 40q + O(q^{10}) \) \( 40q + 16q^{17} - 152q^{25} + 16q^{41} - 216q^{49} - 64q^{65} - 176q^{73} - 432q^{89} - 240q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1152.3.b.a \(2\) \(31.390\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-3iq^{13}-30q^{17}-39q^{25}+\cdots\)
1152.3.b.b \(2\) \(31.390\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+4iq^{13}-2^{4}q^{17}-11q^{25}+\cdots\)
1152.3.b.c \(2\) \(31.390\) \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{11}+2q^{17}-\beta q^{19}+5^{2}q^{25}+\cdots\)
1152.3.b.d \(2\) \(31.390\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-4iq^{13}+2^{4}q^{17}-11q^{25}+\cdots\)
1152.3.b.e \(4\) \(31.390\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{7}-\zeta_{12}q^{11}+\cdots\)
1152.3.b.f \(4\) \(31.390\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+21q^{25}+\cdots\)
1152.3.b.g \(4\) \(31.390\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5\zeta_{8}^{2}q^{11}+5\zeta_{8}q^{13}+\cdots\)
1152.3.b.h \(4\) \(31.390\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{11}+\cdots\)
1152.3.b.i \(8\) \(31.390\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{5}-\beta _{5}q^{7}-\beta _{3}q^{11}-\beta _{2}q^{13}+\cdots\)
1152.3.b.j \(8\) \(31.390\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{24}-\zeta_{24}^{4})q^{5}+\zeta_{24}^{2}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)