Properties

Label 1734.2.h
Level $1734$
Weight $2$
Character orbit 1734.h
Rep. character $\chi_{1734}(733,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $176$
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.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(612\)

Dimensions

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

Total New Old
Modular forms 1368 176 1192
Cusp forms 1080 176 904
Eisenstein series 288 0 288

Trace form

\( 176 q - 16 q^{5} + O(q^{10}) \) \( 176 q - 16 q^{5} + 16 q^{11} + 16 q^{14} - 176 q^{16} + 16 q^{19} + 16 q^{22} + 16 q^{23} + 16 q^{25} - 16 q^{26} - 16 q^{28} - 16 q^{33} + 64 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} - 16 q^{42} - 16 q^{44} - 64 q^{50} + 16 q^{52} - 48 q^{53} - 32 q^{57} - 16 q^{59} + 16 q^{61} - 64 q^{65} - 16 q^{66} - 80 q^{67} - 16 q^{70} + 48 q^{71} - 16 q^{73} + 16 q^{74} + 32 q^{75} - 16 q^{76} + 64 q^{77} + 32 q^{78} - 16 q^{79} + 16 q^{80} + 16 q^{83} + 16 q^{84} + 64 q^{86} + 48 q^{87} + 16 q^{88} - 48 q^{91} + 16 q^{93} + 16 q^{94} - 16 q^{95} + 16 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1734, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(289, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(578, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(867, [\chi])\)\(^{\oplus 2}\)