Properties

Label 618.2.p
Level $618$
Weight $2$
Character orbit 618.p
Rep. character $\chi_{618}(5,\cdot)$
Character field $\Q(\zeta_{102})$
Dimension $1088$
Newform subspaces $1$
Sturm bound $208$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 618 = 2 \cdot 3 \cdot 103 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 618.p (of order \(102\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 309 \)
Character field: \(\Q(\zeta_{102})\)
Newform subspaces: \( 1 \)
Sturm bound: \(208\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(618, [\chi])\).

Total New Old
Modular forms 3456 1088 2368
Cusp forms 3200 1088 2112
Eisenstein series 256 0 256

Trace form

\( 1088 q - 34 q^{4} + 6 q^{6} - 6 q^{7} - 16 q^{9} + O(q^{10}) \) \( 1088 q - 34 q^{4} + 6 q^{6} - 6 q^{7} - 16 q^{9} - 6 q^{12} - 4 q^{15} + 34 q^{16} - 4 q^{19} - 28 q^{21} + 126 q^{25} + 6 q^{28} - 4 q^{30} + 2 q^{33} + 60 q^{36} + 204 q^{37} + 68 q^{39} + 12 q^{43} + 18 q^{45} + 20 q^{46} - 6 q^{48} + 44 q^{49} - 180 q^{55} - 12 q^{57} + 82 q^{58} + 4 q^{60} - 112 q^{61} + 32 q^{63} + 68 q^{64} + 88 q^{66} - 252 q^{67} + 136 q^{69} - 60 q^{70} - 34 q^{73} - 30 q^{75} - 8 q^{76} - 54 q^{78} - 60 q^{79} - 24 q^{81} + 8 q^{82} + 6 q^{84} - 112 q^{85} + 60 q^{87} - 40 q^{88} - 516 q^{91} - 56 q^{93} - 136 q^{94} - 6 q^{96} - 222 q^{97} + 108 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(618, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
618.2.p.a 618.p 309.o $1088$ $4.935$ None \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{102}]$

Decomposition of \(S_{2}^{\mathrm{old}}(618, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(618, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(309, [\chi])\)\(^{\oplus 2}\)