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Properties

Label 3234.2.cf
Level $3234$
Weight $2$
Character orbit 3234.cf
Rep. character $\chi_{3234}(5,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $10752$
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.cf (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
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 10752 21888
Cusp forms 31872 10752 21120
Eisenstein series 768 0 768

Trace form

\( 10752 q + 224 q^{4} - 4 q^{7} + O(q^{10}) \) \( 10752 q + 224 q^{4} - 4 q^{7} - 12 q^{10} - 224 q^{16} + 8 q^{18} + 16 q^{21} - 10 q^{22} - 228 q^{25} - 126 q^{27} - 6 q^{28} - 18 q^{31} + 132 q^{33} + 4 q^{37} - 20 q^{39} - 66 q^{40} - 108 q^{42} - 64 q^{43} + 76 q^{45} + 148 q^{49} + 12 q^{51} + 322 q^{55} + 88 q^{57} - 284 q^{58} + 12 q^{63} - 448 q^{64} + 120 q^{66} + 32 q^{67} + 56 q^{69} + 100 q^{70} + 12 q^{72} + 96 q^{73} + 204 q^{75} - 32 q^{78} - 44 q^{79} - 108 q^{81} - 24 q^{82} + 36 q^{84} - 96 q^{85} + 452 q^{87} + 2 q^{88} + 184 q^{91} + 26 q^{93} - 192 q^{94} + 736 q^{99} + O(q^{100}) \)

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

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