Properties

Label 366.2.a
Level $366$
Weight $2$
Character orbit 366.a
Rep. character $\chi_{366}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $8$
Sturm bound $124$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 366 = 2 \cdot 3 \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 366.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(124\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(366))\).

Total New Old
Modular forms 66 9 57
Cusp forms 59 9 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.

\(2\)\(3\)\(61\)FrickeDim
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(1\)
\(+\)\(-\)\(-\)$+$\(1\)
\(-\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(7\)

Trace form

\( 9 q - q^{2} - q^{3} + 9 q^{4} - 6 q^{5} + q^{6} - 4 q^{7} - q^{8} + 9 q^{9} + O(q^{10}) \) \( 9 q - q^{2} - q^{3} + 9 q^{4} - 6 q^{5} + q^{6} - 4 q^{7} - q^{8} + 9 q^{9} + 2 q^{10} + 4 q^{11} - q^{12} + 2 q^{13} + 6 q^{15} + 9 q^{16} - 2 q^{17} - q^{18} + 4 q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{23} + q^{24} + 15 q^{25} - 6 q^{26} - q^{27} - 4 q^{28} + 10 q^{29} + 6 q^{30} + 4 q^{31} - q^{32} + 4 q^{33} - 2 q^{34} + 16 q^{35} + 9 q^{36} + 14 q^{37} - 12 q^{38} - 6 q^{39} + 2 q^{40} + 22 q^{41} + 4 q^{42} - 16 q^{43} + 4 q^{44} - 6 q^{45} + 8 q^{46} - 8 q^{47} - q^{48} - 11 q^{49} - 31 q^{50} - 14 q^{51} + 2 q^{52} + 2 q^{53} + q^{54} + 8 q^{55} - 12 q^{57} - 18 q^{58} + 4 q^{59} + 6 q^{60} + 5 q^{61} - 12 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{66} - 40 q^{67} - 2 q^{68} + 8 q^{69} - 4 q^{70} - 48 q^{71} - q^{72} - 6 q^{73} - 30 q^{74} - 31 q^{75} + 4 q^{76} - 36 q^{77} + 6 q^{78} - 4 q^{79} - 6 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} - 4 q^{84} - 20 q^{85} + 8 q^{86} - 2 q^{87} + 22 q^{89} + 2 q^{90} - 16 q^{91} + 8 q^{92} - 20 q^{93} + 32 q^{94} + 24 q^{95} + q^{96} - 26 q^{97} - 9 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(366))\) 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 61
366.2.a.a 366.a 1.a $1$ $2.923$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+4q^{7}+\cdots\)
366.2.a.b 366.a 1.a $1$ $2.923$ \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
366.2.a.c 366.a 1.a $1$ $2.923$ \(\Q\) None \(-1\) \(1\) \(1\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-2q^{7}+\cdots\)
366.2.a.d 366.a 1.a $1$ $2.923$ \(\Q\) None \(1\) \(-1\) \(-3\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}-3q^{7}+\cdots\)
366.2.a.e 366.a 1.a $1$ $2.923$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
366.2.a.f 366.a 1.a $1$ $2.923$ \(\Q\) None \(1\) \(1\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
366.2.a.g 366.a 1.a $1$ $2.923$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
366.2.a.h 366.a 1.a $2$ $2.923$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(0\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-2\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(122))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 2}\)