Properties

Label 3234.2.br
Level 3234
Weight 2
Character orbit br
Rep. character \(\chi_{3234}(241,\cdot)\)
Character field \(\Q(\zeta_{42})\)
Dimension 1344
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.br (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 8160 1344 6816
Cusp forms 7968 1344 6624
Eisenstein series 192 0 192

Trace form

\( 1344q - 112q^{4} - 24q^{5} - 112q^{9} + O(q^{10}) \) \( 1344q - 112q^{4} - 24q^{5} - 112q^{9} + 36q^{11} - 16q^{14} - 20q^{15} + 112q^{16} + 56q^{20} + 18q^{22} + 8q^{23} - 108q^{25} + 32q^{26} - 12q^{31} - 6q^{33} - 224q^{36} - 20q^{37} - 88q^{38} + 44q^{42} + 48q^{44} + 88q^{45} - 232q^{47} - 212q^{49} + 112q^{53} - 42q^{55} + 104q^{56} - 84q^{58} - 56q^{59} - 52q^{60} + 224q^{64} + 88q^{70} + 48q^{71} + 24q^{75} - 64q^{77} + 24q^{80} + 112q^{81} + 24q^{82} + 192q^{86} + 30q^{88} - 320q^{89} + 72q^{91} + 16q^{92} - 16q^{93} + 16q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database