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Properties

Label 1734.2.o
Level $1734$
Weight $2$
Character orbit 1734.o
Rep. character $\chi_{1734}(13,\cdot)$
Character field $\Q(\zeta_{68})$
Dimension $1600$
Sturm bound $612$

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Defining parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.o (of order \(68\) and degree \(32\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{68})\)
Sturm bound: \(612\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1734, [\chi])\).

Total New Old
Modular forms 9920 1600 8320
Cusp forms 9664 1600 8064
Eisenstein series 256 0 256

Trace form

\( 1600 q + 100 q^{4} + 4 q^{5} - 8 q^{7} + O(q^{10}) \) \( 1600 q + 100 q^{4} + 4 q^{5} - 8 q^{7} + 4 q^{10} + 8 q^{13} + 8 q^{14} - 100 q^{16} + 12 q^{17} - 4 q^{18} - 4 q^{20} - 8 q^{21} - 8 q^{23} + 68 q^{25} + 8 q^{28} - 4 q^{29} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 16 q^{35} + 12 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} - 4 q^{45} + 144 q^{46} - 20 q^{50} - 8 q^{51} - 8 q^{52} + 136 q^{53} + 48 q^{55} - 8 q^{56} + 8 q^{57} - 4 q^{58} - 20 q^{61} - 8 q^{62} - 8 q^{63} + 100 q^{64} + 16 q^{65} + 96 q^{67} - 12 q^{68} + 16 q^{69} - 24 q^{71} + 4 q^{72} - 4 q^{73} + 12 q^{74} + 256 q^{75} - 136 q^{77} + 8 q^{78} + 432 q^{79} + 4 q^{80} + 100 q^{81} - 20 q^{82} + 136 q^{83} + 8 q^{84} - 164 q^{85} + 136 q^{88} + 32 q^{89} + 4 q^{90} + 16 q^{91} - 128 q^{92} + 272 q^{94} + 4 q^{97} + 36 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1734, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1734, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1734, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(867, [\chi])\)\(^{\oplus 2}\)