↑

Properties

Label 50.4.a
Level $50$
Weight $4$
Character orbit 50.a
Rep. character $\chi_{50}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $30$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 50.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(50))\).

Total New Old
Modular forms 29 5 24
Cusp forms 17 5 12
Eisenstein series 12 0 12

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

\(2\)\(5\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(1\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(4\)
Minus space\(-\)\(1\)

Trace form

\( 5 q - 2 q^{2} + 8 q^{3} + 20 q^{4} + 20 q^{6} + 4 q^{7} - 8 q^{8} + 35 q^{9} + O(q^{10}) \) \( 5 q - 2 q^{2} + 8 q^{3} + 20 q^{4} + 20 q^{6} + 4 q^{7} - 8 q^{8} + 35 q^{9} + 10 q^{11} + 32 q^{12} + 58 q^{13} - 40 q^{14} + 80 q^{16} - 66 q^{17} - 74 q^{18} - 150 q^{19} - 340 q^{21} - 24 q^{22} - 132 q^{23} + 80 q^{24} - 180 q^{26} + 80 q^{27} + 16 q^{28} - 150 q^{29} + 260 q^{31} - 32 q^{32} + 96 q^{33} - 40 q^{34} + 140 q^{36} + 34 q^{37} + 200 q^{38} + 120 q^{39} + 760 q^{41} - 64 q^{42} - 32 q^{43} + 40 q^{44} - 280 q^{46} + 204 q^{47} + 128 q^{48} + 1965 q^{49} - 490 q^{51} + 232 q^{52} - 222 q^{53} - 700 q^{54} - 160 q^{56} - 800 q^{57} + 180 q^{58} - 1300 q^{59} + 1510 q^{61} - 304 q^{62} + 148 q^{63} + 320 q^{64} + 340 q^{66} + 1024 q^{67} - 264 q^{68} - 2380 q^{69} - 3240 q^{71} - 296 q^{72} - 362 q^{73} + 1460 q^{74} - 600 q^{76} + 48 q^{77} - 928 q^{78} - 300 q^{79} - 1195 q^{81} + 876 q^{82} - 72 q^{83} - 1360 q^{84} + 920 q^{86} - 720 q^{87} - 96 q^{88} + 1300 q^{89} + 2760 q^{91} - 528 q^{92} + 1216 q^{93} + 160 q^{94} + 320 q^{96} - 1106 q^{97} + 654 q^{98} + 2920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(50))\) 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
50.4.a.a 50.a 1.a $1$ $2.950$ \(\Q\) None \(-2\) \(-7\) \(0\) \(34\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-7q^{3}+4q^{4}+14q^{6}+34q^{7}+\cdots\)
50.4.a.b 50.a 1.a $1$ $2.950$ \(\Q\) None \(-2\) \(-2\) \(0\) \(-26\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-26q^{7}+\cdots\)
50.4.a.c 50.a 1.a $1$ $2.950$ \(\Q\) None \(-2\) \(8\) \(0\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+8q^{3}+4q^{4}-2^{4}q^{6}+4q^{7}+\cdots\)
50.4.a.d 50.a 1.a $1$ $2.950$ \(\Q\) None \(2\) \(2\) \(0\) \(26\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+26q^{7}+\cdots\)
50.4.a.e 50.a 1.a $1$ $2.950$ \(\Q\) None \(2\) \(7\) \(0\) \(-34\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+7q^{3}+4q^{4}+14q^{6}-34q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(50))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(50)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 2}\)