↑

Properties

Label 3234.2.ck
Level $3234$
Weight $2$
Character orbit 3234.ck
Rep. character $\chi_{3234}(61,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $5376$
Sturm bound $1344$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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