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Properties

Label 1610.2.a
Level $1610$
Weight $2$
Character orbit 1610.a
Rep. character $\chi_{1610}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $19$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1610.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1610))\).

Total New Old
Modular forms 296 45 251
Cusp forms 281 45 236
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.

\(2\)\(5\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(+\)\(-\)\(-\)$+$\(3\)
\(+\)\(-\)\(+\)\(+\)$-$\(4\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(2\)
\(+\)\(-\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)\(-\)$+$\(1\)
\(-\)\(+\)\(-\)\(+\)$+$\(2\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(5\)
\(-\)\(-\)\(-\)\(+\)$-$\(4\)
\(-\)\(-\)\(-\)\(-\)$+$\(1\)
Plus space\(+\)\(15\)
Minus space\(-\)\(30\)

Trace form

\( 45 q - 3 q^{2} - 4 q^{3} + 45 q^{4} + q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 41 q^{9} + O(q^{10}) \) \( 45 q - 3 q^{2} - 4 q^{3} + 45 q^{4} + q^{5} - 4 q^{6} + q^{7} - 3 q^{8} + 41 q^{9} + q^{10} - 4 q^{11} - 4 q^{12} + 14 q^{13} + q^{14} - 4 q^{15} + 45 q^{16} + 10 q^{17} - 7 q^{18} - 4 q^{19} + q^{20} - 4 q^{21} - 12 q^{22} + q^{23} - 4 q^{24} + 45 q^{25} + 14 q^{26} + 8 q^{27} + q^{28} + 22 q^{29} + 4 q^{30} - 3 q^{32} - 6 q^{34} - 3 q^{35} + 41 q^{36} + 6 q^{37} + 12 q^{38} + 40 q^{39} + q^{40} + 18 q^{41} + 4 q^{42} - 28 q^{43} - 4 q^{44} + 13 q^{45} + q^{46} + 32 q^{47} - 4 q^{48} + 45 q^{49} - 3 q^{50} + 8 q^{51} + 14 q^{52} + 38 q^{53} + 8 q^{54} + 12 q^{55} + q^{56} + 64 q^{57} + 22 q^{58} + 36 q^{59} - 4 q^{60} + 14 q^{61} + 16 q^{62} + 13 q^{63} + 45 q^{64} + 6 q^{65} + 32 q^{66} + 28 q^{67} + 10 q^{68} + 4 q^{69} - 3 q^{70} + 40 q^{71} - 7 q^{72} + 18 q^{73} + 14 q^{74} - 4 q^{75} - 4 q^{76} - 4 q^{77} + 8 q^{78} + 16 q^{79} + q^{80} + 5 q^{81} - 14 q^{82} - 20 q^{83} - 4 q^{84} - 14 q^{85} - 20 q^{86} - 88 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 10 q^{91} + q^{92} - 64 q^{93} - 48 q^{94} + 12 q^{95} - 4 q^{96} + 26 q^{97} - 3 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1610))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 7 23
1610.2.a.a 1610.a 1.a $1$ $12.856$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
1610.2.a.b 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
1610.2.a.c 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
1610.2.a.d 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(-2\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
1610.2.a.e 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
1610.2.a.f 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
1610.2.a.g 1610.a 1.a $1$ $12.856$ \(\Q\) None \(1\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}-3q^{9}+\cdots\)
1610.2.a.h 1610.a 1.a $2$ $12.856$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
1610.2.a.i 1610.a 1.a $2$ $12.856$ \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{7}+\cdots\)
1610.2.a.j 1610.a 1.a $2$ $12.856$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-q^{7}+\cdots\)
1610.2.a.k 1610.a 1.a $3$ $12.856$ 3.3.316.1 None \(-3\) \(-2\) \(-3\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
1610.2.a.l 1610.a 1.a $3$ $12.856$ 3.3.148.1 None \(-3\) \(2\) \(-3\) \(-3\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1610.2.a.m 1610.a 1.a $3$ $12.856$ 3.3.564.1 None \(-3\) \(2\) \(-3\) \(3\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1610.2.a.n 1610.a 1.a $3$ $12.856$ 3.3.404.1 None \(3\) \(-2\) \(-3\) \(-3\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
1610.2.a.o 1610.a 1.a $3$ $12.856$ 3.3.148.1 None \(3\) \(4\) \(-3\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
1610.2.a.p 1610.a 1.a $4$ $12.856$ 4.4.25492.1 None \(-4\) \(0\) \(4\) \(-4\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1610.2.a.q 1610.a 1.a $4$ $12.856$ 4.4.63796.1 None \(-4\) \(0\) \(4\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
1610.2.a.r 1610.a 1.a $4$ $12.856$ 4.4.25492.1 None \(4\) \(0\) \(4\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
1610.2.a.s 1610.a 1.a $5$ $12.856$ 5.5.3035380.1 None \(5\) \(0\) \(5\) \(-5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+q^{5}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 2}\)