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Properties

Label 348.3.r
Level $348$
Weight $3$
Character orbit 348.r
Rep. character $\chi_{348}(53,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $120$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 348.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 87 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(348, [\chi])\).

Total New Old
Modular forms 756 120 636
Cusp forms 684 120 564
Eisenstein series 72 0 72

Trace form

\( 120 q - 8 q^{7} - 12 q^{9} + O(q^{10}) \) \( 120 q - 8 q^{7} - 12 q^{9} + 42 q^{13} - 14 q^{15} + 20 q^{19} - 166 q^{21} + 28 q^{25} - 150 q^{27} + 20 q^{31} - 54 q^{33} + 36 q^{37} + 144 q^{39} - 154 q^{43} - 48 q^{45} - 180 q^{49} + 4 q^{51} - 144 q^{55} + 164 q^{57} - 248 q^{61} + 340 q^{63} - 324 q^{67} + 396 q^{69} - 298 q^{73} + 812 q^{75} + 238 q^{79} + 232 q^{81} + 462 q^{85} + 322 q^{87} + 158 q^{91} - 320 q^{93} + 494 q^{97} - 152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(348, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
348.3.r.a 348.r 87.j $120$ $9.482$ None 348.3.r.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{3}^{\mathrm{old}}(348, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(348, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(174, [\chi])\)\(^{\oplus 2}\)