Properties

Label 3234.2.ck
Level 3234
Weight 2
Character orbit ck
Rep. character \(\chi_{3234}(61,\cdot)\)
Character field \(\Q(\zeta_{210})\)
Dimension 5376
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.ck (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 32640 5376 27264
Cusp forms 31872 5376 26496
Eisenstein series 768 0 768

Trace form

\( 5376q + 112q^{4} + 24q^{5} - 20q^{7} + 112q^{9} + O(q^{10}) \) \( 5376q + 112q^{4} + 24q^{5} - 20q^{7} + 112q^{9} - 36q^{11} - 4q^{14} - 30q^{15} - 112q^{16} - 200q^{17} - 56q^{20} - 18q^{22} - 8q^{23} + 108q^{25} - 32q^{26} + 10q^{28} + 40q^{29} - 18q^{31} + 6q^{33} - 40q^{35} + 224q^{36} + 20q^{37} + 88q^{38} + 110q^{40} - 54q^{42} - 68q^{44} - 88q^{45} - 188q^{47} + 152q^{49} + 520q^{51} - 112q^{53} + 42q^{55} - 104q^{56} + 4q^{58} + 56q^{59} + 52q^{60} + 60q^{61} + 280q^{62} - 20q^{63} - 224q^{64} + 60q^{68} + 92q^{70} - 48q^{71} - 240q^{73} + 40q^{74} - 24q^{75} + 164q^{77} + 60q^{79} + 36q^{80} - 112q^{81} + 96q^{82} + 40q^{85} + 288q^{86} + 130q^{88} + 440q^{89} + 68q^{91} - 16q^{92} + 16q^{93} + 140q^{94} + 20q^{95} - 16q^{99} + O(q^{100}) \)

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