Properties

Label 546.2.a
Level $546$
Weight $2$
Character orbit 546.a
Rep. character $\chi_{546}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $10$
Sturm bound $224$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(224\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(546))\).

Total New Old
Modular forms 120 13 107
Cusp forms 105 13 92
Eisenstein series 15 0 15

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

\(2\)\(3\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(-\)$-$\(1\)
\(+\)\(+\)\(-\)\(+\)$-$\(2\)
\(+\)\(-\)\(+\)\(+\)$-$\(1\)
\(+\)\(-\)\(+\)\(-\)$+$\(1\)
\(+\)\(-\)\(-\)\(-\)$-$\(1\)
\(-\)\(+\)\(+\)\(+\)$-$\(1\)
\(-\)\(+\)\(-\)\(-\)$-$\(2\)
\(-\)\(-\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)\(+\)$-$\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(12\)

Trace form

\( 13 q + q^{2} + q^{3} + 13 q^{4} + 6 q^{5} + q^{6} + q^{7} + q^{8} + 13 q^{9} + O(q^{10}) \) \( 13 q + q^{2} + q^{3} + 13 q^{4} + 6 q^{5} + q^{6} + q^{7} + q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + q^{12} + q^{13} + q^{14} + 6 q^{15} + 13 q^{16} + 2 q^{17} + q^{18} + 4 q^{19} + 6 q^{20} - 3 q^{21} + 4 q^{22} + q^{24} + 27 q^{25} + q^{26} + q^{27} + q^{28} + 6 q^{29} - 2 q^{30} + 16 q^{31} + q^{32} - 4 q^{33} + 18 q^{34} - 2 q^{35} + 13 q^{36} - 10 q^{37} + 4 q^{38} + q^{39} + 6 q^{40} + 10 q^{41} + q^{42} + 4 q^{43} + 12 q^{44} + 6 q^{45} - 16 q^{46} - 16 q^{47} + q^{48} + 13 q^{49} - q^{50} + 2 q^{51} + q^{52} + 14 q^{53} + q^{54} + 8 q^{55} + q^{56} - 28 q^{57} + 6 q^{58} + 28 q^{59} + 6 q^{60} - 18 q^{61} - 32 q^{62} + q^{63} + 13 q^{64} - 2 q^{65} - 4 q^{66} - 4 q^{67} + 2 q^{68} + 8 q^{69} - 10 q^{70} - 8 q^{71} + q^{72} - 38 q^{73} + 6 q^{74} - 33 q^{75} + 4 q^{76} + 12 q^{77} - 3 q^{78} + 6 q^{80} + 13 q^{81} - 14 q^{82} - 12 q^{83} - 3 q^{84} - 36 q^{85} - 20 q^{86} - 10 q^{87} + 4 q^{88} - 6 q^{89} + 6 q^{90} - 3 q^{91} - 32 q^{93} - 24 q^{94} - 40 q^{95} + q^{96} - 30 q^{97} + q^{98} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(546))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7 13
546.2.a.a 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.a \(-1\) \(-1\) \(-1\) \(-1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
546.2.a.b 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.b \(-1\) \(1\) \(-2\) \(-1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.c 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.c \(-1\) \(1\) \(1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.d 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.d \(-1\) \(1\) \(3\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.e 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.e \(1\) \(-1\) \(3\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots\)
546.2.a.f 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.f \(1\) \(1\) \(-1\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.g 546.a 1.a $1$ $4.360$ \(\Q\) None 546.2.a.g \(1\) \(1\) \(2\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.h 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{57}) \) None 546.2.a.h \(-2\) \(-2\) \(-1\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta q^{5}+q^{6}+q^{7}+\cdots\)
546.2.a.i 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{41}) \) None 546.2.a.i \(2\) \(-2\) \(-1\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots\)
546.2.a.j 546.a 1.a $2$ $4.360$ \(\Q(\sqrt{17}) \) None 546.2.a.j \(2\) \(2\) \(3\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2-\beta )q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(546))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(546)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 2}\)