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Properties

Label 3136.2.m
Level $3136$
Weight $2$
Character orbit 3136.m
Rep. character $\chi_{3136}(785,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $154$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 960 174 786
Cusp forms 832 154 678
Eisenstein series 128 20 108

Trace form

\( 154 q - 2 q^{3} + 2 q^{5} + O(q^{10}) \) \( 154 q - 2 q^{3} + 2 q^{5} + 2 q^{11} + 2 q^{13} + 12 q^{15} + 4 q^{17} - 10 q^{19} + 16 q^{27} - 18 q^{29} - 16 q^{31} + 4 q^{33} - 6 q^{37} - 10 q^{43} - 2 q^{45} + 16 q^{47} + 56 q^{51} + 10 q^{53} - 30 q^{59} - 14 q^{61} + 12 q^{65} - 10 q^{67} - 20 q^{69} - 18 q^{75} - 8 q^{79} - 70 q^{81} - 42 q^{83} + 16 q^{85} - 4 q^{93} + 52 q^{95} + 4 q^{97} + 74 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3136, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1568, [\chi])\)\(^{\oplus 2}\)