Properties

Label 1584.2.o
Level $1584$
Weight $2$
Character orbit 1584.o
Rep. character $\chi_{1584}(703,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $7$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 44 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(83\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1584, [\chi])\).

Total New Old
Modular forms 312 30 282
Cusp forms 264 30 234
Eisenstein series 48 0 48

Trace form

\( 30 q + O(q^{10}) \) \( 30 q + 6 q^{25} + 30 q^{49} + 12 q^{53} + 48 q^{77} - 24 q^{89} + 48 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1584, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1584.2.o.a 1584.o 44.c $2$ $12.648$ \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) 176.2.e.a \(0\) \(0\) \(-6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{5}-\beta q^{11}+\beta q^{23}+4q^{25}+3\beta q^{31}+\cdots\)
1584.2.o.b 1584.o 44.c $4$ $12.648$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 1584.2.o.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+\beta _{2}q^{7}+(-3+\beta _{1})q^{11}+\cdots\)
1584.2.o.c 1584.o 44.c $4$ $12.648$ \(\Q(\sqrt{6}, \sqrt{-11})\) \(\Q(\sqrt{-33}) \) 1584.2.o.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{7}-\beta _{3}q^{11}+\beta _{2}q^{17}+3\beta _{1}q^{19}+\cdots\)
1584.2.o.d 1584.o 44.c $4$ $12.648$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None 1584.2.o.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}+\beta _{2}q^{7}+(3-\beta _{1})q^{11}-3\beta _{1}q^{13}+\cdots\)
1584.2.o.e 1584.o 44.c $4$ $12.648$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) 176.2.e.b \(0\) \(0\) \(6\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(1+\beta _{3})q^{5}+(2\beta _{1}-\beta _{2})q^{11}+(\beta _{1}+\cdots)q^{23}+\cdots\)
1584.2.o.f 1584.o 44.c $4$ $12.648$ \(\Q(i, \sqrt{10})\) None 528.2.o.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{5}+\beta _{3}q^{7}+(-\beta _{1}+\beta _{3})q^{11}+\cdots\)
1584.2.o.g 1584.o 44.c $8$ $12.648$ 8.0.454201344.7 None 528.2.o.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{5}+\beta _{6}q^{7}+(\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1584, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1584, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(132, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(176, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(396, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(528, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(792, [\chi])\)\(^{\oplus 2}\)