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Properties

Label 348.2.n
Level $348$
Weight $2$
Character orbit 348.n
Rep. character $\chi_{348}(13,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $36$
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.n (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
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 396 36 360
Cusp forms 324 36 288
Eisenstein series 72 0 72

Trace form

\( 36 q - 4 q^{7} + 6 q^{9} + O(q^{10}) \) \( 36 q - 4 q^{7} + 6 q^{9} - 6 q^{13} + 14 q^{15} + 26 q^{23} + 24 q^{25} + 18 q^{29} + 28 q^{31} - 8 q^{33} + 80 q^{35} - 28 q^{37} - 14 q^{43} - 56 q^{47} - 38 q^{49} - 26 q^{51} - 16 q^{53} + 14 q^{55} - 16 q^{57} - 52 q^{59} - 56 q^{61} - 10 q^{63} - 60 q^{65} - 60 q^{67} - 28 q^{69} - 50 q^{71} + 14 q^{73} - 14 q^{77} + 14 q^{79} - 6 q^{81} + 64 q^{83} + 14 q^{85} + 32 q^{87} - 14 q^{89} - 2 q^{91} + 4 q^{93} + 14 q^{97} + O(q^{100}) \)

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.n.a 348.n 29.e $36$ $2.779$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{14}]$

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

\( S_{2}^{\mathrm{old}}(348, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 2}\)