Properties

Label 1734.2.f
Level $1734$
Weight $2$
Character orbit 1734.f
Rep. character $\chi_{1734}(829,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $15$
Sturm bound $612$
Trace bound $21$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 15 \)
Sturm bound: \(612\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 684 92 592
Cusp forms 540 92 448
Eisenstein series 144 0 144

Trace form

\( 92q - 92q^{4} + 4q^{5} - 8q^{7} + O(q^{10}) \) \( 92q - 92q^{4} + 4q^{5} - 8q^{7} + 4q^{10} - 8q^{13} + 8q^{14} + 92q^{16} - 4q^{18} - 4q^{20} - 8q^{21} - 8q^{23} + 8q^{28} - 4q^{29} - 8q^{30} - 8q^{31} + 24q^{33} + 16q^{35} + 12q^{37} - 32q^{38} + 8q^{39} - 4q^{40} + 20q^{41} - 4q^{45} + 8q^{46} - 32q^{47} + 12q^{50} + 8q^{52} + 16q^{55} - 8q^{56} + 8q^{57} - 4q^{58} - 20q^{61} - 8q^{62} - 8q^{63} - 92q^{64} + 16q^{65} + 8q^{67} + 32q^{69} - 24q^{71} + 4q^{72} - 4q^{73} + 12q^{74} - 16q^{75} + 8q^{78} + 24q^{79} + 4q^{80} - 92q^{81} - 20q^{82} + 8q^{84} + 32q^{86} - 32q^{89} + 4q^{90} + 16q^{91} + 8q^{92} + 4q^{97} + 4q^{98} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1734.2.f.a \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
1734.2.f.b \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\zeta_{8}q^{6}+\cdots\)
1734.2.f.c \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+3\zeta_{8}q^{5}+\cdots\)
1734.2.f.d \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}-q^{4}-\zeta_{8}q^{6}+\cdots\)
1734.2.f.e \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots\)
1734.2.f.f \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots\)
1734.2.f.g \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-q^{4}+4\zeta_{8}q^{5}+\cdots\)
1734.2.f.h \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+2\zeta_{8}q^{5}+\cdots\)
1734.2.f.i \(4\) \(13.846\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(-8\) \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
1734.2.f.j \(8\) \(13.846\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(8\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{5}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
1734.2.f.k \(8\) \(13.846\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(-8\) \(8\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(-1+2\zeta_{16}+\cdots)q^{5}+\cdots\)
1734.2.f.l \(8\) \(13.846\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(-8\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}q^{3}-q^{4}+(1+2\zeta_{16}+\cdots)q^{5}+\cdots\)
1734.2.f.m \(8\) \(13.846\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(-8\) \(q-\zeta_{16}^{3}q^{2}-\zeta_{16}q^{3}-q^{4}+(1+\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
1734.2.f.n \(12\) \(13.846\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots\)
1734.2.f.o \(12\) \(13.846\) 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}-\beta _{10}q^{3}-q^{4}+(2\beta _{10}-\beta _{11})q^{5}+\cdots\)

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

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