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Properties

Label 3136.2.bf
Level $3136$
Weight $2$
Character orbit 3136.bf
Rep. character $\chi_{3136}(447,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $660$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.bf (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3136, [\chi])\).

Total New Old
Modular forms 2760 684 2076
Cusp forms 2616 660 1956
Eisenstein series 144 24 120

Trace form

\( 660 q + 14 q^{5} - 116 q^{9} + O(q^{10}) \) \( 660 q + 14 q^{5} - 116 q^{9} + 14 q^{13} - 14 q^{17} - 2 q^{21} + 92 q^{25} + 10 q^{29} - 14 q^{33} + 50 q^{37} - 14 q^{41} + 14 q^{45} - 12 q^{49} + 10 q^{53} - 40 q^{57} + 70 q^{61} - 30 q^{65} + 14 q^{69} - 14 q^{73} + 2 q^{77} - 172 q^{81} + 78 q^{85} - 14 q^{89} + 56 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3136, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3136, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)