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Properties

Label 1734.2.n
Level $1734$
Weight $2$
Character orbit 1734.n
Rep. character $\chi_{1734}(67,\cdot)$
Character field $\Q(\zeta_{34})$
Dimension $800$
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.n (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 289 \)
Character field: \(\Q(\zeta_{34})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 4960 800 4160
Cusp forms 4832 800 4032
Eisenstein series 128 0 128

Trace form

\( 800 q - 2 q^{2} - 50 q^{4} + 34 q^{5} - 2 q^{8} + 50 q^{9} + O(q^{10}) \) \( 800 q - 2 q^{2} - 50 q^{4} + 34 q^{5} - 2 q^{8} + 50 q^{9} + 8 q^{13} - 50 q^{16} + 2 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{21} + 16 q^{25} + 12 q^{26} - 4 q^{30} - 2 q^{32} - 4 q^{33} + 2 q^{34} - 16 q^{35} + 50 q^{36} + 128 q^{38} + 4 q^{42} + 4 q^{43} + 68 q^{44} - 68 q^{46} + 44 q^{47} + 50 q^{49} - 10 q^{50} - 8 q^{51} + 42 q^{52} - 48 q^{53} - 8 q^{55} + 16 q^{59} + 68 q^{63} - 50 q^{64} - 96 q^{67} + 2 q^{68} - 16 q^{69} + 2 q^{72} + 4 q^{76} - 60 q^{77} - 136 q^{79} - 50 q^{81} - 28 q^{83} + 4 q^{84} + 16 q^{85} - 16 q^{86} + 16 q^{87} - 68 q^{88} - 36 q^{89} + 272 q^{91} - 68 q^{92} + 20 q^{93} - 144 q^{94} - 14 q^{98} + O(q^{100}) \)

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

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