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Properties

Label 3136.2.u
Level $3136$
Weight $2$
Character orbit 3136.u
Rep. character $\chi_{3136}(449,\cdot)$
Character field $\Q(\zeta_{7})$
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.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
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

\( 660 q + 10 q^{5} - 116 q^{9} + O(q^{10}) \) \( 660 q + 10 q^{5} - 116 q^{9} + 26 q^{13} - 10 q^{17} + 14 q^{21} - 112 q^{25} + 10 q^{29} + 2 q^{33} - 30 q^{37} - 10 q^{41} - 22 q^{45} - 12 q^{49} + 10 q^{53} - 40 q^{57} - 30 q^{61} + 10 q^{65} - 2 q^{69} - 10 q^{73} + 22 q^{77} - 12 q^{81} + 38 q^{85} - 42 q^{89} + 56 q^{93} - 56 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)