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Properties

Label 1734.2.b
Level $1734$
Weight $2$
Character orbit 1734.b
Rep. character $\chi_{1734}(577,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $12$
Sturm bound $612$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(612\)
Trace bound: \(13\)
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 342 46 296
Cusp forms 270 46 224
Eisenstein series 72 0 72

Trace form

\( 46 q - 2 q^{2} + 46 q^{4} - 2 q^{8} - 46 q^{9} + O(q^{10}) \) \( 46 q - 2 q^{2} + 46 q^{4} - 2 q^{8} - 46 q^{9} + 16 q^{13} - 8 q^{15} + 46 q^{16} + 2 q^{18} - 4 q^{19} + 4 q^{21} - 54 q^{25} + 12 q^{26} - 4 q^{30} - 2 q^{32} + 4 q^{33} - 46 q^{36} + 8 q^{38} + 4 q^{42} - 20 q^{43} - 8 q^{47} - 62 q^{49} + 6 q^{50} + 16 q^{52} + 4 q^{53} + 8 q^{55} - 16 q^{59} - 8 q^{60} + 46 q^{64} - 4 q^{67} - 8 q^{69} - 16 q^{70} + 2 q^{72} - 4 q^{76} - 8 q^{77} + 46 q^{81} + 24 q^{83} + 4 q^{84} + 8 q^{87} - 4 q^{89} + 20 q^{93} - 24 q^{94} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1734.2.b.a 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.i \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}+q^{4}+4iq^{5}-iq^{6}+\cdots\)
1734.2.b.b 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.c \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-iq^{3}+q^{4}+2iq^{5}+iq^{6}+\cdots\)
1734.2.b.c 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.k \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-iq^{3}+q^{4}+3iq^{5}+iq^{6}+\cdots\)
1734.2.b.d 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+4iq^{5}+iq^{6}+\cdots\)
1734.2.b.e 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.c \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{6}+iq^{7}+q^{8}+\cdots\)
1734.2.b.f 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 102.2.a.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-iq^{3}+q^{4}-iq^{6}+2iq^{7}+\cdots\)
1734.2.b.g 1734.b 17.b $2$ $13.846$ \(\Q(\sqrt{-1}) \) None 1734.2.a.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}+iq^{5}+iq^{6}+4iq^{7}+\cdots\)
1734.2.b.h 1734.b 17.b $4$ $13.846$ \(\Q(\zeta_{8})\) None 102.2.f.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\zeta_{8}q^{3}+q^{4}+(2\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
1734.2.b.i 1734.b 17.b $6$ $13.846$ 6.0.419904.1 None 1734.2.a.r \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
1734.2.b.j 1734.b 17.b $6$ $13.846$ 6.0.419904.1 None 1734.2.a.p \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
1734.2.b.k 1734.b 17.b $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.a \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\zeta_{16}q^{3}+q^{4}+(\zeta_{16}^{2}+\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
1734.2.b.l 1734.b 17.b $8$ $13.846$ \(\Q(\zeta_{16})\) None 102.2.h.b \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}-\zeta_{16}q^{3}+q^{4}+(2\zeta_{16}+\zeta_{16}^{2}+\cdots)q^{5}+\cdots\)

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

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