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Properties

Label 3234.2.ca
Level $3234$
Weight $2$
Character orbit 3234.ca
Rep. character $\chi_{3234}(13,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $2688$
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.ca (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 16320 2688 13632
Cusp forms 15936 2688 13248
Eisenstein series 384 0 384

Trace form

\( 2688 q - 112 q^{4} + 20 q^{7} - 112 q^{9} + O(q^{10}) \) \( 2688 q - 112 q^{4} + 20 q^{7} - 112 q^{9} + 12 q^{11} + 4 q^{14} + 30 q^{15} + 112 q^{16} + 140 q^{17} + 56 q^{20} + 18 q^{22} - 16 q^{23} - 120 q^{25} + 56 q^{26} - 10 q^{28} - 40 q^{29} - 20 q^{35} + 112 q^{36} + 40 q^{37} + 56 q^{38} + 70 q^{40} - 18 q^{42} - 52 q^{44} - 56 q^{45} + 308 q^{47} + 88 q^{49} + 200 q^{51} - 56 q^{53} - 126 q^{55} - 40 q^{56} + 50 q^{58} - 56 q^{59} + 20 q^{60} + 140 q^{62} + 20 q^{63} - 112 q^{64} + 4 q^{70} + 48 q^{71} + 420 q^{73} + 80 q^{74} - 20 q^{77} + 120 q^{79} + 112 q^{81} - 40 q^{85} - 180 q^{86} - 76 q^{88} - 56 q^{89} + 136 q^{91} + 16 q^{92} + 32 q^{93} - 140 q^{94} + 40 q^{95} + 16 q^{99} + O(q^{100}) \)

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

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