Properties

Label 1152.3.g
Level $1152$
Weight $3$
Character orbit 1152.g
Rep. character $\chi_{1152}(127,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $6$
Sturm bound $576$
Trace bound $13$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1152.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 4 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(576\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(13\)

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

\( 40q + O(q^{10}) \) \( 40q - 16q^{17} + 248q^{25} - 176q^{41} - 344q^{49} + 160q^{65} - 464q^{73} + 48q^{89} + 368q^{97} + O(q^{100}) \)

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.g.a \(4\) \(31.390\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q+(-2+\zeta_{8}^{3})q^{5}+(-\zeta_{8}-\zeta_{8}^{2})q^{7}+\cdots\)
1152.3.g.b \(4\) \(31.390\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) \(q+(2+\zeta_{8}^{2})q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+(-\zeta_{8}+\cdots)q^{11}+\cdots\)
1152.3.g.c \(8\) \(31.390\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-16\) \(0\) \(q+(-2+\zeta_{24})q^{5}-\zeta_{24}^{6}q^{7}+(\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)
1152.3.g.d \(8\) \(31.390\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(-6+\beta _{7})q^{13}+\cdots\)
1152.3.g.e \(8\) \(31.390\) 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{5}-\beta _{5}q^{7}+\beta _{1}q^{11}+(6-\beta _{7})q^{13}+\cdots\)
1152.3.g.f \(8\) \(31.390\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(16\) \(0\) \(q+(2-\zeta_{24}^{2})q^{5}-\zeta_{24}^{4}q^{7}+(\zeta_{24}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 2}\)