↑

Properties

Label 246.2.a
Level $246$
Weight $2$
Character orbit 246.a
Rep. character $\chi_{246}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $7$
Sturm bound $84$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 246 = 2 \cdot 3 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 246.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(84\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(246))\).

Total New Old
Modular forms 46 7 39
Cusp forms 39 7 32
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.

\(2\)\(3\)\(41\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(-\)\(+\)$-$\(2\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(6\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(246))\) 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 41
246.2.a.a 246.a 1.a $1$ $1.964$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+2q^{7}+\cdots\)
246.2.a.b 246.a 1.a $1$ $1.964$ \(\Q\) None \(-1\) \(-1\) \(3\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-2q^{7}+\cdots\)
246.2.a.c 246.a 1.a $1$ $1.964$ \(\Q\) None \(-1\) \(1\) \(-2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+2q^{7}+\cdots\)
246.2.a.d 246.a 1.a $1$ $1.964$ \(\Q\) None \(-1\) \(1\) \(3\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+2q^{7}+\cdots\)
246.2.a.e 246.a 1.a $1$ $1.964$ \(\Q\) None \(1\) \(-1\) \(1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
246.2.a.f 246.a 1.a $1$ $1.964$ \(\Q\) None \(1\) \(1\) \(-2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots\)
246.2.a.g 246.a 1.a $1$ $1.964$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(246))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(246)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(123))\)\(^{\oplus 2}\)