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Properties

Label 576.2.bd
Level $576$
Weight $2$
Character orbit 576.bd
Rep. character $\chi_{576}(37,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $312$
Newform subspaces $3$
Sturm bound $192$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Newform subspaces: \( 3 \)
Sturm bound: \(192\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(576, [\chi])\).

Total New Old
Modular forms 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} + O(q^{10}) \) \( 312 q + 8 q^{2} - 8 q^{4} + 8 q^{5} - 8 q^{7} + 8 q^{8} - 8 q^{10} + 8 q^{11} - 8 q^{13} + 8 q^{14} - 8 q^{16} + 8 q^{17} - 8 q^{19} + 8 q^{20} + 8 q^{23} - 8 q^{25} + 48 q^{26} + 32 q^{28} + 8 q^{29} + 48 q^{32} + 32 q^{34} + 8 q^{35} - 8 q^{37} + 48 q^{38} + 32 q^{40} + 8 q^{41} - 8 q^{43} + 16 q^{44} - 8 q^{46} + 8 q^{47} - 8 q^{49} - 16 q^{50} + 40 q^{52} + 8 q^{53} - 72 q^{55} - 48 q^{56} - 80 q^{58} + 72 q^{59} - 8 q^{61} - 56 q^{62} + 88 q^{64} + 16 q^{65} + 8 q^{67} - 40 q^{68} + 88 q^{70} + 72 q^{71} - 8 q^{73} - 48 q^{74} - 40 q^{76} + 8 q^{77} - 40 q^{79} - 80 q^{80} - 88 q^{82} + 8 q^{83} - 8 q^{85} - 96 q^{86} - 88 q^{88} + 8 q^{89} - 8 q^{91} - 144 q^{92} - 104 q^{94} - 128 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(576, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.2.bd.a 576.bd 64.i $56$ $4.599$ None \(8\) \(0\) \(8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
576.2.bd.b 576.bd 64.i $128$ $4.599$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
576.2.bd.c 576.bd 64.i $128$ $4.599$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(576, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(576, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)