↑

Properties

Label 348.2.s
Level $348$
Weight $2$
Character orbit 348.s
Rep. character $\chi_{348}(23,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 348.s (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

\( 336 q - 10 q^{4} - 7 q^{6} - 10 q^{9} + O(q^{10}) \) \( 336 q - 10 q^{4} - 7 q^{6} - 10 q^{9} - 18 q^{10} - 24 q^{12} - 20 q^{13} - 26 q^{16} + 32 q^{18} - 14 q^{21} - 12 q^{22} - 13 q^{24} - 76 q^{28} - 10 q^{30} + 2 q^{33} - 12 q^{34} + 9 q^{36} - 36 q^{37} - 14 q^{40} + 40 q^{42} - 38 q^{45} - 96 q^{46} - 34 q^{48} + 4 q^{49} - 76 q^{52} + 21 q^{54} - 36 q^{57} - 98 q^{58} + 62 q^{60} - 4 q^{61} - 106 q^{64} + 27 q^{66} - 6 q^{69} - 208 q^{70} - 106 q^{72} - 28 q^{73} + 32 q^{76} + 23 q^{78} - 50 q^{81} + 26 q^{82} + 111 q^{84} + 96 q^{85} + 4 q^{88} - 107 q^{90} - 142 q^{93} + 52 q^{94} + 14 q^{96} + 20 q^{97} + O(q^{100}) \)

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.s.a 348.s 348.s $336$ $2.779$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$