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Properties

Label 348.2.x
Level $348$
Weight $2$
Character orbit 348.x
Rep. character $\chi_{348}(19,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $360$
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.x (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 116 \)
Character field: \(\Q(\zeta_{28})\)
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 768 360 408
Cusp forms 672 360 312
Eisenstein series 96 0 96

Trace form

\( 360 q - 4 q^{2} - 4 q^{8} + O(q^{10}) \) \( 360 q - 4 q^{2} - 4 q^{8} - 4 q^{14} - 8 q^{16} - 20 q^{17} - 4 q^{18} + 12 q^{24} + 20 q^{25} + 20 q^{26} - 32 q^{30} + 16 q^{32} + 36 q^{37} - 44 q^{40} - 20 q^{41} - 24 q^{44} + 8 q^{46} - 112 q^{48} + 44 q^{49} - 104 q^{50} - 68 q^{52} - 96 q^{53} - 156 q^{56} - 192 q^{58} - 144 q^{60} - 12 q^{61} - 196 q^{62} - 120 q^{66} - 216 q^{68} - 60 q^{70} - 24 q^{72} + 60 q^{73} + 44 q^{74} + 40 q^{76} + 16 q^{77} - 36 q^{78} + 60 q^{81} - 40 q^{82} - 40 q^{84} + 56 q^{88} - 36 q^{89} - 36 q^{94} - 144 q^{97} + 124 q^{98} + O(q^{100}) \)

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.x.a 348.x 116.l $360$ $2.779$ None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{2}^{\mathrm{old}}(348, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(348, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)