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Properties

Label 544.2.cc
Level $544$
Weight $2$
Character orbit 544.cc
Rep. character $\chi_{544}(79,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $128$
Newform subspaces $3$
Sturm bound $144$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 544 = 2^{5} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 544.cc (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 136 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(544, [\chi])\).

Total New Old
Modular forms 640 160 480
Cusp forms 512 128 384
Eisenstein series 128 32 96

Trace form

\( 128 q + 16 q^{3} - 16 q^{9} + 16 q^{11} - 16 q^{17} + 16 q^{19} - 16 q^{25} + 16 q^{27} + 32 q^{35} - 16 q^{41} + 16 q^{43} - 16 q^{49} + 16 q^{51} - 48 q^{57} + 16 q^{59} + 64 q^{65} - 96 q^{73} + 16 q^{75}+ \cdots - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(544, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
544.2.cc.a 544.cc 136.s $8$ $4.344$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) 136.2.s.b \(0\) \(-8\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$ \(q+(-1-\zeta_{16}+\zeta_{16}^{2}+\zeta_{16}^{4}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
544.2.cc.b 544.cc 136.s $8$ $4.344$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-2}) \) 136.2.s.a \(0\) \(8\) \(0\) \(0\) $\mathrm{U}(1)[D_{16}]$ \(q+(1+\zeta_{16}+\zeta_{16}^{2}-\zeta_{16}^{4}+\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
544.2.cc.c 544.cc 136.s $112$ $4.344$ None 136.2.s.c \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(544, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(544, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)