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Properties

Label 348.2.t
Level $348$
Weight $2$
Character orbit 348.t
Rep. character $\chi_{348}(35,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 348.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 348 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(348, [\chi])\).

Total New Old
Modular forms 384 384 0
Cusp forms 336 336 0
Eisenstein series 48 48 0

Trace form

\( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} + O(q^{10}) \) \( 336 q - 10 q^{4} - 3 q^{6} - 10 q^{9} - 14 q^{10} - 20 q^{13} - 26 q^{16} - 56 q^{18} - 14 q^{21} - 40 q^{22} + 3 q^{24} + 40 q^{25} - 36 q^{28} - 6 q^{30} - 22 q^{33} - 8 q^{34} + 9 q^{36} - 28 q^{37} - 14 q^{40} - 74 q^{42} - 22 q^{45} + 14 q^{48} + 4 q^{49} - 4 q^{52} - 31 q^{54} - 12 q^{57} - 106 q^{58} - 42 q^{60} - 28 q^{61} - 94 q^{64} - 7 q^{66} - 14 q^{69} + 70 q^{72} - 28 q^{73} - 84 q^{76} - 9 q^{78} - 50 q^{81} - 46 q^{82} - 35 q^{84} - 168 q^{85} - 60 q^{88} + 119 q^{90} + 122 q^{93} + 36 q^{94} + 2 q^{96} - 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(348, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
348.2.t.a 348.t 348.t $336$ $2.779$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$