Properties

Label 1734.2.a
Level $1734$
Weight $2$
Character orbit 1734.a
Rep. character $\chi_{1734}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $23$
Sturm bound $612$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1734.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 23 \)
Sturm bound: \(612\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1734))\).

Total New Old
Modular forms 342 45 297
Cusp forms 271 45 226
Eisenstein series 71 0 71

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(9\)
Plus space\(+\)\(14\)
Minus space\(-\)\(31\)

Trace form

\( 45q + q^{2} - q^{3} + 45q^{4} + 6q^{5} - q^{6} + q^{8} + 45q^{9} + O(q^{10}) \) \( 45q + q^{2} - q^{3} + 45q^{4} + 6q^{5} - q^{6} + q^{8} + 45q^{9} - 2q^{10} + 4q^{11} - q^{12} + 10q^{13} + 2q^{15} + 45q^{16} + q^{18} + 6q^{20} - 4q^{21} + 4q^{22} - q^{24} + 47q^{25} - 2q^{26} - q^{27} + 14q^{29} + 6q^{30} + 8q^{31} + q^{32} + 8q^{33} + 45q^{36} - 2q^{37} + 4q^{38} - 6q^{39} - 2q^{40} - 6q^{41} + 4q^{42} + 8q^{43} + 4q^{44} + 6q^{45} - 8q^{47} - q^{48} + 69q^{49} + 15q^{50} + 10q^{52} - 2q^{53} - q^{54} + 4q^{57} + 6q^{58} + 4q^{59} + 2q^{60} + 6q^{61} - 24q^{62} + 45q^{64} - 28q^{65} + 4q^{66} + 40q^{67} + 16q^{69} + 16q^{70} + q^{72} - 14q^{73} + 6q^{74} + 17q^{75} + 8q^{77} + 10q^{78} + 8q^{79} + 6q^{80} + 45q^{81} - 14q^{82} + 4q^{83} - 4q^{84} - 12q^{86} + 10q^{87} + 4q^{88} + 42q^{89} - 2q^{90} - 16q^{91} - 4q^{93} + 24q^{94} + 24q^{95} - q^{96} - 6q^{97} + 9q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1734))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 17
1734.2.a.a \(1\) \(13.846\) \(\Q\) None \(-1\) \(-1\) \(-1\) \(4\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
1734.2.a.b \(1\) \(13.846\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\)
1734.2.a.c \(1\) \(13.846\) \(\Q\) None \(-1\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+q^{7}-q^{8}+\cdots\)
1734.2.a.d \(1\) \(13.846\) \(\Q\) None \(-1\) \(-1\) \(2\) \(2\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
1734.2.a.e \(1\) \(13.846\) \(\Q\) None \(-1\) \(1\) \(-2\) \(-2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1734.2.a.f \(1\) \(13.846\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
1734.2.a.g \(1\) \(13.846\) \(\Q\) None \(-1\) \(1\) \(1\) \(-4\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
1734.2.a.h \(1\) \(13.846\) \(\Q\) None \(-1\) \(1\) \(4\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+4q^{5}-q^{6}+2q^{7}+\cdots\)
1734.2.a.i \(1\) \(13.846\) \(\Q\) None \(1\) \(-1\) \(-4\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
1734.2.a.j \(1\) \(13.846\) \(\Q\) None \(1\) \(-1\) \(2\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
1734.2.a.k \(1\) \(13.846\) \(\Q\) None \(1\) \(-1\) \(3\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+4q^{7}+\cdots\)
1734.2.a.l \(1\) \(13.846\) \(\Q\) None \(1\) \(1\) \(-3\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-4q^{7}+\cdots\)
1734.2.a.m \(1\) \(13.846\) \(\Q\) None \(1\) \(1\) \(4\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+3q^{7}+\cdots\)
1734.2.a.n \(2\) \(13.846\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(4\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(2+\beta )q^{5}-q^{6}+\cdots\)
1734.2.a.o \(2\) \(13.846\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-4\) \(-4\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
1734.2.a.p \(3\) \(13.846\) \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(-6\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
1734.2.a.q \(3\) \(13.846\) \(\Q(\zeta_{18})^+\) None \(-3\) \(3\) \(6\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}-q^{6}+\cdots\)
1734.2.a.r \(3\) \(13.846\) \(\Q(\zeta_{18})^+\) None \(3\) \(-3\) \(-6\) \(3\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}-q^{6}+\cdots\)
1734.2.a.s \(3\) \(13.846\) \(\Q(\zeta_{18})^+\) None \(3\) \(3\) \(6\) \(-3\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(2-\beta _{1})q^{5}+q^{6}+\cdots\)
1734.2.a.t \(4\) \(13.846\) \(\Q(\zeta_{16})^+\) None \(-4\) \(-4\) \(8\) \(0\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+(2+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.u \(4\) \(13.846\) \(\Q(\zeta_{16})^+\) None \(-4\) \(4\) \(-8\) \(0\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-2-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.v \(4\) \(13.846\) \(\Q(\zeta_{16})^+\) None \(4\) \(-4\) \(0\) \(-8\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
1734.2.a.w \(4\) \(13.846\) \(\Q(\zeta_{16})^+\) None \(4\) \(4\) \(0\) \(8\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(\beta _{2}+\beta _{3})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1734))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1734)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 2}\)