Properties

Label 546.2.c
Level $546$
Weight $2$
Character orbit 546.c
Rep. character $\chi_{546}(337,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $5$
Sturm bound $224$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(224\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(546, [\chi])\).

Total New Old
Modular forms 120 12 108
Cusp forms 104 12 92
Eisenstein series 16 0 16

Trace form

\( 12 q - 12 q^{4} + 12 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{4} + 12 q^{9} + 16 q^{13} + 12 q^{16} + 16 q^{17} - 8 q^{22} - 8 q^{23} + 4 q^{25} + 24 q^{29} + 8 q^{30} + 8 q^{35} - 12 q^{36} - 16 q^{38} - 8 q^{39} - 4 q^{42} - 24 q^{43} - 12 q^{49} + 16 q^{51} - 16 q^{52} + 40 q^{53} - 64 q^{55} + 16 q^{61} - 12 q^{64} - 24 q^{65} + 16 q^{66} - 16 q^{68} - 16 q^{69} - 16 q^{74} + 32 q^{77} + 4 q^{78} + 16 q^{79} + 12 q^{81} - 8 q^{82} - 8 q^{87} + 8 q^{88} + 4 q^{91} + 8 q^{92} - 8 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(546, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
546.2.c.a 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}-iq^{5}-iq^{6}+iq^{7}+\cdots\)
546.2.c.b 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}+2iq^{5}+iq^{6}+\cdots\)
546.2.c.c 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}-iq^{5}+iq^{6}-iq^{7}+\cdots\)
546.2.c.d 546.c 13.b $2$ $4.360$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{3}-q^{4}-3iq^{5}+iq^{6}+\cdots\)
546.2.c.e 546.c 13.b $4$ $4.360$ \(\Q(i, \sqrt{17})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-q^{3}-q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(546, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(546, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)