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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.2.d.a 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.b 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.c 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots\)
1152.2.d.d 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots\)
1152.2.d.e 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.f 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.g 1152.d 8.b $4$ $9.199$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots\)
1152.2.d.h 1152.d 8.b $4$ $9.199$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots\)

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

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