Properties

Label 3234.2.ba
Level 3234
Weight 2
Character orbit 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

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

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database