Properties

Label 579.2.a
Level $579$
Weight $2$
Character orbit 579.a
Rep. character $\chi_{579}(1,\cdot)$
Character field $\Q$
Dimension $33$
Newform subspaces $7$
Sturm bound $129$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 579 = 3 \cdot 193 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 579.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(129\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(579))\).

Total New Old
Modular forms 66 33 33
Cusp forms 63 33 30
Eisenstein series 3 0 3

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

\(3\)\(193\)FrickeDim
\(+\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(11\)
\(-\)\(+\)\(-\)\(13\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(9\)
Minus space\(-\)\(24\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(579))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 193
579.2.a.a 579.a 1.a $1$ $4.623$ \(\Q\) None 579.2.a.a \(-1\) \(1\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
579.2.a.b 579.a 1.a $1$ $4.623$ \(\Q\) None 579.2.a.b \(2\) \(-1\) \(2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+2q^{5}-2q^{6}+\cdots\)
579.2.a.c 579.a 1.a $2$ $4.623$ \(\Q(\sqrt{2}) \) None 579.2.a.c \(-2\) \(-2\) \(-4\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+(-2+\beta )q^{5}+q^{6}+\cdots\)
579.2.a.d 579.a 1.a $3$ $4.623$ 3.3.257.1 None 579.2.a.d \(0\) \(-3\) \(-4\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
579.2.a.e 579.a 1.a $3$ $4.623$ \(\Q(\zeta_{18})^+\) None 579.2.a.e \(0\) \(3\) \(-6\) \(-9\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-2+\beta _{1}+\cdots)q^{5}+\cdots\)
579.2.a.f 579.a 1.a $10$ $4.623$ 10.10.\(\cdots\).1 None 579.2.a.f \(2\) \(-10\) \(8\) \(-10\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{5}q^{2}-q^{3}+(2-\beta _{4}-\beta _{6}-\beta _{9})q^{4}+\cdots\)
579.2.a.g 579.a 1.a $13$ $4.623$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 579.2.a.g \(2\) \(13\) \(6\) \(15\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(579))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(579)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(193))\)\(^{\oplus 2}\)