Properties

Label 1152.3.m
Level $1152$
Weight $3$
Character orbit 1152.m
Rep. character $\chi_{1152}(415,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $6$
Sturm bound $576$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 832 84 748
Cusp forms 704 76 628
Eisenstein series 128 8 120

Trace form

\( 76q - 4q^{5} + O(q^{10}) \) \( 76q - 4q^{5} + 4q^{13} + 8q^{17} + 28q^{29} - 92q^{37} + 356q^{49} - 164q^{53} + 68q^{61} + 40q^{65} + 24q^{77} - 216q^{85} - 8q^{97} + O(q^{100}) \)

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.m.a \(6\) \(31.390\) 6.0.399424.1 None \(0\) \(0\) \(-2\) \(-4\) \(q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)
1152.3.m.b \(6\) \(31.390\) 6.0.399424.1 None \(0\) \(0\) \(-2\) \(4\) \(q+(-1+\beta _{1}-\beta _{2}-\beta _{4})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1152.3.m.c \(16\) \(31.390\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{5}-\beta _{3}q^{7}+(-2-2\beta _{2}+\beta _{5}+\cdots)q^{11}+\cdots\)
1152.3.m.d \(16\) \(31.390\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}-\beta _{8}q^{7}+(\beta _{4}+\beta _{14})q^{11}+\cdots\)
1152.3.m.e \(16\) \(31.390\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{5}+\beta _{8}q^{7}+(-\beta _{4}-\beta _{14})q^{11}+\cdots\)
1152.3.m.f \(16\) \(31.390\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{11}q^{5}+\beta _{3}q^{7}+(2+2\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)