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Properties

Label 3136.2.j
Level $3136$
Weight $2$
Character orbit 3136.j
Rep. character $\chi_{3136}(783,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $152$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 960 168 792
Cusp forms 832 152 680
Eisenstein series 128 16 112

Trace form

\( 152 q + O(q^{10}) \) \( 152 q - 12 q^{11} + 8 q^{23} + 8 q^{29} + 20 q^{37} - 8 q^{39} + 16 q^{43} - 68 q^{51} + 20 q^{53} + 8 q^{65} - 68 q^{67} + 80 q^{71} - 80 q^{81} - 28 q^{85} - 20 q^{93} + 96 q^{99} + O(q^{100}) \)

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

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