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Properties

Label 348.6.n
Level $348$
Weight $6$
Character orbit 348.n
Rep. character $\chi_{348}(13,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $156$
Sturm bound $360$

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Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 348.n (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(348, [\chi])\).

Total New Old
Modular forms 1836 156 1680
Cusp forms 1764 156 1608
Eisenstein series 72 0 72

Trace form

\( 156 q - 120 q^{5} + 76 q^{7} + 2106 q^{9} + O(q^{10}) \) \( 156 q - 120 q^{5} + 76 q^{7} + 2106 q^{9} - 1154 q^{13} - 1386 q^{15} + 130 q^{23} - 18716 q^{25} + 21906 q^{29} + 5740 q^{31} + 9432 q^{33} + 9712 q^{35} - 33796 q^{37} - 12334 q^{43} - 24300 q^{45} - 4984 q^{47} - 15530 q^{49} + 74934 q^{51} + 25732 q^{53} - 130634 q^{55} - 63648 q^{57} + 57772 q^{59} - 22960 q^{61} + 15390 q^{63} + 300120 q^{65} + 281348 q^{67} + 120708 q^{69} - 144778 q^{71} - 156114 q^{73} + 536270 q^{77} - 41594 q^{79} - 170586 q^{81} + 153008 q^{83} + 373114 q^{85} - 236016 q^{87} - 199906 q^{89} + 149726 q^{91} + 7380 q^{93} - 332794 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(348, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(348, [\chi])\) into lower level spaces

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