Properties

Label 3234.2.bc
Level 3234
Weight 2
Character orbit bc
Rep. character \(\chi_{3234}(307,\cdot)\)
Character field \(\Q(\zeta_{14})\)
Dimension 672
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.bc (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
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 672 3408
Cusp forms 3984 672 3312
Eisenstein series 96 0 96

Trace form

\( 672q + 112q^{4} + 112q^{9} + O(q^{10}) \) \( 672q + 112q^{4} + 112q^{9} - 12q^{11} + 16q^{14} + 20q^{15} - 112q^{16} - 56q^{20} - 18q^{22} + 16q^{23} + 120q^{25} - 56q^{26} - 112q^{36} - 40q^{37} - 56q^{38} + 28q^{42} + 12q^{44} + 56q^{45} + 112q^{47} - 88q^{49} + 56q^{53} + 126q^{55} + 40q^{56} + 56q^{59} - 20q^{60} + 112q^{64} - 4q^{70} - 48q^{71} + 100q^{77} - 112q^{81} - 120q^{86} - 24q^{88} + 56q^{89} - 96q^{91} - 16q^{92} - 32q^{93} - 16q^{99} + O(q^{100}) \)

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