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Properties

Label 3234.2.ba
Level $3234$
Weight $2$
Character orbit 3234.ba
Rep. character $\chi_{3234}(419,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1104$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.ba (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4080 1104 2976
Cusp forms 3984 1104 2880
Eisenstein series 96 0 96

Trace form

\( 1104 q + 184 q^{4} + 28 q^{6} - 12 q^{7} + 20 q^{9} + O(q^{10}) \) \( 1104 q + 184 q^{4} + 28 q^{6} - 12 q^{7} + 20 q^{9} - 24 q^{15} - 184 q^{16} + 4 q^{21} - 168 q^{25} + 12 q^{28} - 16 q^{30} - 20 q^{36} + 108 q^{37} + 24 q^{39} - 84 q^{42} - 40 q^{43} + 120 q^{46} + 24 q^{51} + 84 q^{52} - 60 q^{57} + 20 q^{58} + 24 q^{60} + 308 q^{61} + 28 q^{63} + 184 q^{64} + 72 q^{67} + 32 q^{70} + 168 q^{75} + 56 q^{79} - 20 q^{81} + 80 q^{84} + 128 q^{85} + 84 q^{90} + 8 q^{91} - 20 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)