Properties

Label 3234.2.bh
Level 3234
Weight 2
Character orbit bh
Rep. character \(\chi_{3234}(331,\cdot)\)
Character field \(\Q(\zeta_{21})\)
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.bh (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8160 1104 7056
Cusp forms 7968 1104 6864
Eisenstein series 192 0 192

Trace form

\( 1104q + 92q^{4} + 92q^{9} + O(q^{10}) \) \( 1104q + 92q^{4} + 92q^{9} + 92q^{16} - 8q^{19} + 8q^{21} + 84q^{25} + 32q^{29} + 4q^{33} - 24q^{34} + 32q^{35} - 184q^{36} - 44q^{37} - 16q^{38} + 64q^{39} + 160q^{41} + 48q^{42} + 104q^{47} + 24q^{49} + 32q^{50} + 104q^{53} - 32q^{57} + 52q^{58} + 208q^{59} + 104q^{61} - 184q^{64} + 8q^{66} - 24q^{69} + 40q^{70} + 32q^{71} - 16q^{73} - 8q^{75} + 16q^{76} + 8q^{77} - 80q^{78} + 8q^{79} + 92q^{81} + 16q^{82} + 192q^{83} - 16q^{84} - 16q^{86} - 24q^{87} - 40q^{89} + 248q^{91} + 16q^{93} - 16q^{94} - 32q^{95} + 104q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database