Properties

Label 1573.2.a
Level $1573$
Weight $2$
Character orbit 1573.a
Rep. character $\chi_{1573}(1,\cdot)$
Character field $\Q$
Dimension $109$
Newform subspaces $19$
Sturm bound $308$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1573 = 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1573.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(308\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1573))\).

Total New Old
Modular forms 166 109 57
Cusp forms 143 109 34
Eisenstein series 23 0 23

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

\(11\)\(13\)FrickeDim
\(+\)\(+\)$+$\(25\)
\(+\)\(-\)$-$\(29\)
\(-\)\(+\)$-$\(30\)
\(-\)\(-\)$+$\(25\)
Plus space\(+\)\(50\)
Minus space\(-\)\(59\)

Trace form

\( 109 q - 3 q^{2} - 4 q^{3} + 111 q^{4} - 2 q^{5} + 4 q^{6} - 8 q^{7} - 3 q^{8} + 105 q^{9} + O(q^{10}) \) \( 109 q - 3 q^{2} - 4 q^{3} + 111 q^{4} - 2 q^{5} + 4 q^{6} - 8 q^{7} - 3 q^{8} + 105 q^{9} + 2 q^{10} - 8 q^{12} - q^{13} + 16 q^{14} - 4 q^{15} + 103 q^{16} - 2 q^{17} + 9 q^{18} + 10 q^{20} + 12 q^{21} - 16 q^{23} + 36 q^{24} + 83 q^{25} + 3 q^{26} - 16 q^{27} - 12 q^{28} + 10 q^{29} + 48 q^{30} + 4 q^{31} + 21 q^{32} + 26 q^{34} + 28 q^{35} + 115 q^{36} - 30 q^{37} + 4 q^{38} - 4 q^{39} + 14 q^{40} - 14 q^{41} - 24 q^{42} - 20 q^{43} - 30 q^{45} + 4 q^{47} - 24 q^{48} + 85 q^{49} - 25 q^{50} + 12 q^{51} - 7 q^{52} - 22 q^{53} - 36 q^{54} - 4 q^{56} - 52 q^{57} - 26 q^{58} - 28 q^{60} - 2 q^{61} - 28 q^{62} + 87 q^{64} - 2 q^{65} - 20 q^{67} - 2 q^{68} - 24 q^{69} - 4 q^{70} + 28 q^{71} + q^{72} - 38 q^{73} - 50 q^{74} + 8 q^{75} + 36 q^{76} - 8 q^{78} - 12 q^{79} - 66 q^{80} + 101 q^{81} - 46 q^{82} + 28 q^{83} - 44 q^{84} - 40 q^{85} - 12 q^{86} + 20 q^{87} + 6 q^{89} - 14 q^{90} - 124 q^{92} - 24 q^{93} - 32 q^{94} + 52 q^{95} + 64 q^{96} - 50 q^{97} + 17 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 13
1573.2.a.a 1573.a 1.a $1$ $12.560$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots\)
1573.2.a.b 1573.a 1.a $1$ $12.560$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+2q^{7}-2q^{9}+2q^{12}+\cdots\)
1573.2.a.c 1573.a 1.a $1$ $12.560$ \(\Q\) None \(1\) \(-1\) \(-2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\)
1573.2.a.d 1573.a 1.a $2$ $12.560$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+(-2+2\beta )q^{3}+3q^{4}+\cdots\)
1573.2.a.e 1573.a 1.a $2$ $12.560$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-2\beta q^{3}+3q^{4}+(-2+\cdots)q^{5}+\cdots\)
1573.2.a.f 1573.a 1.a $4$ $12.560$ 4.4.1957.1 None \(-3\) \(0\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1}-\beta _{2})q^{2}+(-\beta _{2}-\beta _{3})q^{3}+\cdots\)
1573.2.a.g 1573.a 1.a $4$ $12.560$ 4.4.11344.1 None \(-2\) \(0\) \(-2\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1573.2.a.h 1573.a 1.a $4$ $12.560$ 4.4.11344.1 None \(2\) \(0\) \(-2\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
1573.2.a.i 1573.a 1.a $5$ $12.560$ 5.5.535120.1 None \(-3\) \(-1\) \(-2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1573.2.a.j 1573.a 1.a $5$ $12.560$ 5.5.558733.1 None \(-3\) \(-1\) \(1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1573.2.a.k 1573.a 1.a $5$ $12.560$ 5.5.535120.1 None \(3\) \(-1\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1573.2.a.l 1573.a 1.a $5$ $12.560$ 5.5.558733.1 None \(3\) \(-1\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
1573.2.a.m 1573.a 1.a $6$ $12.560$ 6.6.194616205.1 None \(0\) \(3\) \(1\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1573.2.a.n 1573.a 1.a $8$ $12.560$ 8.8.661518125.1 None \(-1\) \(-5\) \(-5\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
1573.2.a.o 1573.a 1.a $8$ $12.560$ 8.8.661518125.1 None \(1\) \(-5\) \(-5\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(-1+\beta _{7})q^{3}+(1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
1573.2.a.p 1573.a 1.a $10$ $12.560$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-6\) \(-2\) \(2\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1573.2.a.q 1573.a 1.a $10$ $12.560$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(6\) \(-2\) \(2\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{3}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1573.2.a.r 1573.a 1.a $14$ $12.560$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(9\) \(9\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1573.2.a.s 1573.a 1.a $14$ $12.560$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(9\) \(9\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1573))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1573)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 2}\)