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Properties

Label 348.2.l
Level $348$
Weight $2$
Character orbit 348.l
Rep. character $\chi_{348}(17,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $20$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q(i)\)
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 132 20 112
Cusp forms 108 20 88
Eisenstein series 24 0 24

Trace form

\( 20 q + O(q^{10}) \) \( 20 q + 10 q^{15} - 4 q^{19} + 4 q^{21} + 20 q^{25} + 6 q^{27} - 16 q^{31} - 4 q^{37} - 10 q^{39} - 8 q^{43} - 8 q^{45} - 4 q^{49} - 12 q^{55} + 20 q^{61} + 52 q^{69} - 28 q^{73} - 26 q^{75} - 16 q^{79} - 40 q^{81} - 80 q^{85} - 36 q^{87} + 44 q^{97} + 18 q^{99} + O(q^{100}) \)

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.l.a 348.l 87.f $20$ $2.779$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{14}q^{3}+\beta _{19}q^{5}-\beta _{8}q^{7}-\beta _{3}q^{9}+\cdots\)

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

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