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Properties

Label 3136.2.bb
Level $3136$
Weight $2$
Character orbit 3136.bb
Rep. character $\chi_{3136}(177,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $304$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3136 = 2^{6} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3136.bb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 1920 336 1584
Cusp forms 1664 304 1360
Eisenstein series 256 32 224

Trace form

\( 304 q - 2 q^{3} + 2 q^{5} + O(q^{10}) \) \( 304 q - 2 q^{3} + 2 q^{5} - 10 q^{11} + 8 q^{13} + 32 q^{15} + 4 q^{17} - 2 q^{19} - 20 q^{27} - 48 q^{29} + 20 q^{31} + 4 q^{33} + 18 q^{37} + 28 q^{45} - 44 q^{47} - 6 q^{51} - 14 q^{53} - 18 q^{59} + 2 q^{61} + 4 q^{65} + 50 q^{67} + 20 q^{69} - 24 q^{75} - 4 q^{79} + 92 q^{81} + 32 q^{83} - 36 q^{85} + 26 q^{93} + 20 q^{95} + 16 q^{97} + 72 q^{99} + O(q^{100}) \)

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

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