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Properties

Label 3136.2.bt
Level $3136$
Weight $2$
Character orbit 3136.bt
Rep. character $\chi_{3136}(113,\cdot)$
Character field $\Q(\zeta_{28})$
Dimension $1320$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.bt (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 784 \)
Character field: \(\Q(\zeta_{28})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 5472 1368 4104
Cusp forms 5280 1320 3960
Eisenstein series 192 48 144

Trace form

\( 1320 q + 10 q^{3} - 10 q^{5} + O(q^{10}) \) \( 1320 q + 10 q^{3} - 10 q^{5} + 10 q^{11} - 10 q^{13} + 20 q^{15} - 20 q^{17} + 24 q^{19} - 18 q^{21} + 22 q^{27} - 10 q^{29} + 192 q^{31} - 20 q^{33} + 10 q^{35} - 10 q^{37} + 10 q^{43} - 18 q^{45} + 60 q^{47} - 24 q^{49} + 38 q^{51} - 10 q^{53} - 22 q^{59} - 10 q^{61} + 52 q^{63} - 20 q^{65} + 48 q^{67} - 22 q^{69} + 2 q^{75} - 26 q^{77} + 48 q^{79} + 168 q^{81} - 30 q^{83} + 10 q^{85} + 186 q^{91} - 40 q^{93} + 68 q^{95} - 48 q^{97} + 48 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)