Properties

Label 63.3.l
Level $63$
Weight $3$
Character orbit 63.l
Rep. character $\chi_{63}(13,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $1$
Sturm bound $24$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 63.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

Total New Old
Modular forms 36 36 0
Cusp forms 28 28 0
Eisenstein series 8 8 0

Trace form

\( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9} + O(q^{10}) \) \( 28 q - 2 q^{2} - 26 q^{4} + 8 q^{8} - 24 q^{9} + 4 q^{11} + 34 q^{14} - 54 q^{15} - 42 q^{16} + 54 q^{18} + 18 q^{21} + 14 q^{22} + 4 q^{23} + 28 q^{25} + 20 q^{28} - 38 q^{29} + 168 q^{30} - 168 q^{32} - 264 q^{35} + 234 q^{36} + 36 q^{37} - 228 q^{39} - 192 q^{42} - 66 q^{43} + 108 q^{44} - 40 q^{46} - 38 q^{49} + 196 q^{50} + 246 q^{51} + 520 q^{53} + 332 q^{56} - 198 q^{57} - 34 q^{58} + 96 q^{60} + 48 q^{63} + 72 q^{64} - 102 q^{65} + 68 q^{67} + 102 q^{70} - 332 q^{71} - 1308 q^{72} - 616 q^{74} + 334 q^{77} - 168 q^{78} + 146 q^{79} + 276 q^{81} + 498 q^{84} + 78 q^{85} - 340 q^{86} - 74 q^{88} - 384 q^{91} + 606 q^{92} + 534 q^{93} - 360 q^{95} - 1076 q^{98} + 900 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
63.3.l.a 63.l 63.l $28$ $1.717$ None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$