Properties

Label 494.2.a
Level $494$
Weight $2$
Character orbit 494.a
Rep. character $\chi_{494}(1,\cdot)$
Character field $\Q$
Dimension $17$
Newform subspaces $8$
Sturm bound $140$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 494 = 2 \cdot 13 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 494.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(140\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(494))\).

Total New Old
Modular forms 74 17 57
Cusp forms 67 17 50
Eisenstein series 7 0 7

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

\(2\)\(13\)\(19\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(5\)
\(+\)\(-\)\(+\)$-$\(3\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(-\)\(+\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(2\)
Minus space\(-\)\(15\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(494))\) 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 13 19
494.2.a.a 494.a 1.a $1$ $3.945$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots\)
494.2.a.b 494.a 1.a $1$ $3.945$ \(\Q\) None \(-1\) \(0\) \(2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
494.2.a.c 494.a 1.a $1$ $3.945$ \(\Q\) None \(-1\) \(3\) \(-3\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+3q^{7}+\cdots\)
494.2.a.d 494.a 1.a $1$ $3.945$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-3q^{7}+\cdots\)
494.2.a.e 494.a 1.a $3$ $3.945$ \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(3\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+q^{4}+\cdots\)
494.2.a.f 494.a 1.a $3$ $3.945$ 3.3.361.1 None \(-3\) \(-1\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{1}-\beta _{2})q^{5}+\cdots\)
494.2.a.g 494.a 1.a $3$ $3.945$ \(\Q(\zeta_{14})^+\) None \(3\) \(5\) \(5\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(2-\beta _{1})q^{3}+q^{4}+(2+\beta _{2})q^{5}+\cdots\)
494.2.a.h 494.a 1.a $4$ $3.945$ 4.4.16609.1 None \(4\) \(2\) \(2\) \(7\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(1-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(494))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(494)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(247))\)\(^{\oplus 2}\)