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Properties

Label 1722.2.a
Level $1722$
Weight $2$
Character orbit 1722.a
Rep. character $\chi_{1722}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $26$
Sturm bound $672$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1722 = 2 \cdot 3 \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1722.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(672\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1722))\).

Total New Old
Modular forms 344 41 303
Cusp forms 329 41 288
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.

\(2\)\(3\)\(7\)\(41\)FrickeDim
\(+\)\(+\)\(+\)\(+\)$+$\(4\)
\(+\)\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(+\)\(-\)\(-\)$+$\(3\)
\(+\)\(-\)\(+\)\(+\)$-$\(3\)
\(+\)\(-\)\(+\)\(-\)$+$\(2\)
\(+\)\(-\)\(-\)\(+\)$+$\(1\)
\(+\)\(-\)\(-\)\(-\)$-$\(4\)
\(-\)\(+\)\(+\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)\(-\)$+$\(3\)
\(-\)\(+\)\(-\)\(+\)$+$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(4\)
\(-\)\(-\)\(+\)\(+\)$+$\(1\)
\(-\)\(-\)\(+\)\(-\)$-$\(4\)
\(-\)\(-\)\(-\)\(+\)$-$\(6\)
Plus space\(+\)\(15\)
Minus space\(-\)\(26\)

Trace form

\( 41 q + q^{2} + q^{3} + 41 q^{4} + 6 q^{5} + q^{6} + q^{7} + q^{8} + 41 q^{9} + O(q^{10}) \) \( 41 q + q^{2} + q^{3} + 41 q^{4} + 6 q^{5} + q^{6} + q^{7} + q^{8} + 41 q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + 14 q^{13} + q^{14} + 6 q^{15} + 41 q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + 6 q^{20} + q^{21} + 4 q^{22} - 8 q^{23} + q^{24} + 71 q^{25} - 2 q^{26} + q^{27} + q^{28} + 14 q^{29} - 2 q^{30} - 8 q^{31} + q^{32} + 4 q^{33} + 2 q^{34} + 6 q^{35} + 41 q^{36} + 14 q^{37} + 4 q^{38} - 2 q^{39} + 6 q^{40} + q^{41} + q^{42} + 36 q^{43} + 12 q^{44} + 6 q^{45} + 8 q^{46} + 16 q^{47} + q^{48} + 41 q^{49} + 31 q^{50} + 10 q^{51} + 14 q^{52} + 6 q^{53} + q^{54} - 24 q^{55} + q^{56} - 12 q^{57} + 6 q^{58} - 52 q^{59} + 6 q^{60} - 10 q^{61} + 16 q^{62} + q^{63} + 41 q^{64} - 28 q^{65} - 4 q^{66} - 20 q^{67} + 2 q^{68} + 24 q^{69} - 2 q^{70} - 40 q^{71} + q^{72} + 2 q^{73} + 6 q^{74} - q^{75} + 4 q^{76} - 20 q^{77} + 14 q^{78} + 16 q^{79} + 6 q^{80} + 41 q^{81} + q^{82} - 44 q^{83} + q^{84} - 20 q^{85} - 20 q^{86} + 22 q^{87} + 4 q^{88} - 54 q^{89} + 6 q^{90} + 14 q^{91} - 8 q^{92} + 24 q^{93} - 32 q^{94} - 24 q^{95} + q^{96} + 34 q^{97} + q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1722))\) 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 3 7 41
1722.2.a.a 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
1722.2.a.b 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
1722.2.a.c 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
1722.2.a.d 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(-1\) \(3\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
1722.2.a.e 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(-1\) \(4\) \(1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots\)
1722.2.a.f 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(1\) \(1\) \(1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
1722.2.a.g 1722.a 1.a $1$ $13.750$ \(\Q\) None \(-1\) \(1\) \(3\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
1722.2.a.h 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(-4\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots\)
1722.2.a.i 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
1722.2.a.j 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
1722.2.a.k 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
1722.2.a.l 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(1\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
1722.2.a.m 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(-1\) \(4\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}-q^{7}+\cdots\)
1722.2.a.n 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
1722.2.a.o 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
1722.2.a.p 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(1\) \(2\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
1722.2.a.q 1722.a 1.a $1$ $13.750$ \(\Q\) None \(1\) \(1\) \(4\) \(-1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}-q^{7}+\cdots\)
1722.2.a.r 1722.a 1.a $2$ $13.750$ \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots\)
1722.2.a.s 1722.a 1.a $2$ $13.750$ \(\Q(\sqrt{17}) \) None \(-2\) \(2\) \(-2\) \(-2\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
1722.2.a.t 1722.a 1.a $2$ $13.750$ \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(-1\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
1722.2.a.u 1722.a 1.a $2$ $13.750$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(3\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots\)
1722.2.a.v 1722.a 1.a $2$ $13.750$ \(\Q(\sqrt{17}) \) None \(2\) \(2\) \(-3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
1722.2.a.w 1722.a 1.a $3$ $13.750$ 3.3.940.1 None \(-3\) \(-3\) \(-3\) \(3\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}+q^{6}+\cdots\)
1722.2.a.x 1722.a 1.a $3$ $13.750$ 3.3.316.1 None \(-3\) \(3\) \(-2\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
1722.2.a.y 1722.a 1.a $3$ $13.750$ 3.3.940.1 None \(-3\) \(3\) \(2\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\)
1722.2.a.z 1722.a 1.a $5$ $13.750$ 5.5.2620729.1 None \(5\) \(5\) \(4\) \(5\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{2})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1722))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1722)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(246))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(861))\)\(^{\oplus 2}\)