↑

Properties

Label 3234.2.c
Level $3234$
Weight $2$
Character orbit 3234.c
Rep. character $\chi_{3234}(197,\cdot)$
Character field $\Q$
Dimension $164$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 704 164 540
Cusp forms 640 164 476
Eisenstein series 64 0 64

Trace form

\( 164 q - 4 q^{3} + 164 q^{4} + 12 q^{9} + O(q^{10}) \) \( 164 q - 4 q^{3} + 164 q^{4} + 12 q^{9} - 4 q^{12} + 8 q^{15} + 164 q^{16} - 140 q^{25} - 4 q^{27} - 8 q^{31} - 8 q^{33} - 8 q^{34} + 12 q^{36} - 16 q^{37} + 8 q^{45} - 4 q^{48} - 16 q^{55} + 40 q^{58} + 8 q^{60} + 164 q^{64} + 20 q^{66} - 32 q^{67} + 48 q^{69} + 92 q^{75} - 40 q^{78} + 20 q^{81} + 16 q^{82} + 8 q^{93} + 64 q^{97} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \)