Properties

Label 1152.2.d
Level $1152$
Weight $2$
Character orbit 1152.d
Rep. character $\chi_{1152}(577,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $8$
Sturm bound $384$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

Total New Old
Modular forms 224 20 204
Cusp forms 160 20 140
Eisenstein series 64 0 64

Trace form

\( 20q + O(q^{10}) \) \( 20q + 8q^{17} - 28q^{25} - 24q^{41} + 52q^{49} + 32q^{65} - 56q^{73} + 8q^{89} + 72q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1152.2.d.a \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) \(q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.b \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.c \(2\) \(9.199\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots\)
1152.2.d.d \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots\)
1152.2.d.e \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.f \(2\) \(9.199\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) \(q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.g \(4\) \(9.199\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots\)
1152.2.d.h \(4\) \(9.199\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

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