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Properties

Label 196.6.m
Level $196$
Weight $6$
Character orbit 196.m
Rep. character $\chi_{196}(9,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $276$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 196.m (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(196, [\chi])\).

Total New Old
Modular forms 1716 276 1440
Cusp forms 1644 276 1368
Eisenstein series 72 0 72

Trace form

\( 276 q + 9 q^{3} + 61 q^{5} + 28 q^{7} + 3302 q^{9} + O(q^{10}) \) \( 276 q + 9 q^{3} + 61 q^{5} + 28 q^{7} + 3302 q^{9} - 642 q^{11} + 724 q^{13} - 96 q^{15} + 2386 q^{17} - 3287 q^{19} + 1127 q^{21} + 374 q^{23} + 13554 q^{25} - 20913 q^{27} + 4406 q^{29} + 4837 q^{31} + 24439 q^{33} + 20755 q^{35} - 29492 q^{37} + 9563 q^{39} + 50584 q^{41} - 54276 q^{43} - 104291 q^{45} - 5930 q^{47} - 51310 q^{49} - 55479 q^{51} - 133268 q^{53} - 87979 q^{55} - 94839 q^{57} + 72391 q^{59} + 145456 q^{61} + 38535 q^{63} + 6054 q^{65} - 27839 q^{67} - 160278 q^{69} + 75425 q^{71} + 96752 q^{73} + 341168 q^{75} + 83482 q^{77} + 81299 q^{79} + 604265 q^{81} - 391394 q^{83} + 184862 q^{85} - 1341828 q^{87} - 281067 q^{89} - 442862 q^{91} + 205954 q^{93} + 875947 q^{95} + 1229920 q^{97} + 1041548 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(196, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(196, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)