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Properties

Label 3234.2.cc
Level $3234$
Weight $2$
Character orbit 3234.cc
Rep. character $\chi_{3234}(125,\cdot)$
Character field $\Q(\zeta_{70})$
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.cc (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
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 5376 10944
Cusp forms 15936 5376 10560
Eisenstein series 384 0 384

Trace form

\( 5376 q - 224 q^{4} + 4 q^{7} + O(q^{10}) \) \( 5376 q - 224 q^{4} + 4 q^{7} + 224 q^{16} + 16 q^{18} + 20 q^{21} + 10 q^{22} + 216 q^{25} + 126 q^{27} + 6 q^{28} + 8 q^{37} - 40 q^{39} - 42 q^{40} + 108 q^{42} + 64 q^{43} - 28 q^{45} + 152 q^{49} + 24 q^{51} + 14 q^{55} - 88 q^{57} + 230 q^{58} + 42 q^{63} - 224 q^{64} + 64 q^{67} - 56 q^{69} - 16 q^{70} + 24 q^{72} + 32 q^{78} - 88 q^{79} + 36 q^{81} + 96 q^{85} + 112 q^{87} + 4 q^{88} - 184 q^{91} + 52 q^{93} + 336 q^{94} - 736 q^{99} + O(q^{100}) \)

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

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