Properties

Label 549.2.a
Level $549$
Weight $2$
Character orbit 549.a
Rep. character $\chi_{549}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $9$
Sturm bound $124$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 549 = 3^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 549.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(124\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(549))\).

Total New Old
Modular forms 66 25 41
Cusp forms 59 25 34
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.

\(3\)\(61\)FrickeDim
\(+\)\(+\)$+$\(2\)
\(+\)\(-\)$-$\(8\)
\(-\)\(+\)$-$\(9\)
\(-\)\(-\)$+$\(6\)
Plus space\(+\)\(8\)
Minus space\(-\)\(17\)

Trace form

\( 25 q + q^{2} + 27 q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} + O(q^{10}) \) \( 25 q + q^{2} + 27 q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} + 4 q^{10} - 2 q^{13} + 20 q^{14} + 39 q^{16} - 12 q^{17} + 8 q^{19} + 2 q^{20} - 4 q^{22} + 4 q^{23} + 11 q^{25} + 2 q^{26} - 28 q^{28} + 8 q^{29} + 6 q^{31} + 17 q^{32} - 30 q^{34} + 4 q^{35} + 8 q^{37} - 30 q^{38} - 6 q^{40} + 6 q^{41} + 14 q^{43} + 34 q^{44} - 20 q^{46} + 8 q^{47} + 21 q^{49} + 11 q^{50} - 30 q^{52} - 10 q^{53} + 2 q^{55} + 32 q^{56} + 26 q^{58} - 18 q^{59} + 3 q^{61} + 4 q^{62} + 55 q^{64} + 4 q^{65} + 14 q^{67} - 32 q^{68} - 60 q^{70} - 14 q^{71} - 2 q^{73} - 46 q^{74} + 16 q^{76} - 24 q^{77} + 32 q^{79} - 2 q^{80} - 22 q^{82} + 32 q^{83} - 26 q^{85} + 44 q^{86} - 24 q^{88} + 2 q^{89} + 42 q^{91} - 38 q^{92} - 8 q^{94} + 40 q^{95} - 10 q^{97} - 53 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(549))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 61
549.2.a.a 549.a 1.a $1$ $4.384$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots\)
549.2.a.b 549.a 1.a $1$ $4.384$ \(\Q\) None \(1\) \(0\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{7}-3q^{8}-4q^{11}+\cdots\)
549.2.a.c 549.a 1.a $1$ $4.384$ \(\Q\) None \(1\) \(0\) \(3\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{5}+q^{7}-3q^{8}+3q^{10}+\cdots\)
549.2.a.d 549.a 1.a $2$ $4.384$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+\beta q^{5}-q^{7}-\beta q^{8}+3q^{10}+\cdots\)
549.2.a.e 549.a 1.a $2$ $4.384$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
549.2.a.f 549.a 1.a $3$ $4.384$ 3.3.148.1 None \(-1\) \(0\) \(-6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-2q^{5}-2\beta _{2}q^{7}+\cdots\)
549.2.a.g 549.a 1.a $3$ $4.384$ 3.3.148.1 None \(-1\) \(0\) \(1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
549.2.a.h 549.a 1.a $6$ $4.384$ 6.6.91407488.1 None \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
549.2.a.i 549.a 1.a $6$ $4.384$ 6.6.337383424.1 None \(0\) \(0\) \(0\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(549))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(549)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(183))\)\(^{\oplus 2}\)