Properties

Label 714.2.a
Level $714$
Weight $2$
Character orbit 714.a
Rep. character $\chi_{714}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $13$
Sturm bound $288$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(288\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(714))\).

Total New Old
Modular forms 152 17 135
Cusp forms 137 17 120
Eisenstein series 15 0 15

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

\(2\)\(3\)\(7\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(3\)
Plus space\(+\)\(3\)
Minus space\(-\)\(14\)

Trace form

\( 17q + q^{2} + q^{3} + 17q^{4} + 6q^{5} + q^{6} + q^{7} + q^{8} + 17q^{9} + O(q^{10}) \) \( 17q + q^{2} + q^{3} + 17q^{4} + 6q^{5} + q^{6} + q^{7} + q^{8} + 17q^{9} + 6q^{10} + 12q^{11} + q^{12} + 6q^{13} + q^{14} - 2q^{15} + 17q^{16} + q^{17} + q^{18} + 12q^{19} + 6q^{20} + q^{21} + 4q^{22} - 8q^{23} + q^{24} + 23q^{25} - 2q^{26} + q^{27} + q^{28} + 14q^{29} + 6q^{30} + 16q^{31} + q^{32} + 4q^{33} + q^{34} - 10q^{35} + 17q^{36} + 30q^{37} - 12q^{38} + 14q^{39} + 6q^{40} + 10q^{41} + q^{42} + 4q^{43} + 12q^{44} + 6q^{45} - 8q^{46} - 16q^{47} + q^{48} + 17q^{49} - q^{50} - 3q^{51} + 6q^{52} - 42q^{53} + q^{54} - 24q^{55} + q^{56} + 12q^{57} - 10q^{58} - 36q^{59} - 2q^{60} - 2q^{61} - 32q^{62} + q^{63} + 17q^{64} - 12q^{65} - 4q^{66} + 28q^{67} + q^{68} + 6q^{70} - 24q^{71} + q^{72} - 22q^{73} + 22q^{74} + 31q^{75} + 12q^{76} + 12q^{77} + 6q^{78} + 6q^{80} + 17q^{81} - 22q^{82} + 4q^{83} + q^{84} - 10q^{85} - 4q^{86} - 10q^{87} + 4q^{88} + 26q^{89} + 6q^{90} + 6q^{91} - 8q^{92} + 16q^{93} - 40q^{95} + q^{96} + 2q^{97} + q^{98} + 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(714))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7 17
714.2.a.a \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.b \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
714.2.a.c \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(1\) \(1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.d \(1\) \(5.701\) \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
714.2.a.e \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.f \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
714.2.a.g \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.h \(1\) \(5.701\) \(\Q\) None \(1\) \(-1\) \(3\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
714.2.a.i \(1\) \(5.701\) \(\Q\) None \(1\) \(1\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
714.2.a.j \(2\) \(5.701\) \(\Q(\sqrt{33}) \) None \(-2\) \(2\) \(-3\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
714.2.a.k \(2\) \(5.701\) \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(1\) \(-2\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots\)
714.2.a.l \(2\) \(5.701\) \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(3\) \(-2\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
714.2.a.m \(2\) \(5.701\) \(\Q(\sqrt{6}) \) None \(2\) \(2\) \(4\) \(2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(714))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(714)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(357))\)\(^{\oplus 2}\)