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Properties

Label 539.2.m
Level $539$
Weight $2$
Character orbit 539.m
Rep. character $\chi_{539}(195,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(539, [\chi])\).

Total New Old
Modular forms 256 176 80
Cusp forms 192 144 48
Eisenstein series 64 32 32

Trace form

\( 144 q + 10 q^{2} + 34 q^{4} - 40 q^{8} + 22 q^{9} + O(q^{10}) \) \( 144 q + 10 q^{2} + 34 q^{4} - 40 q^{8} + 22 q^{9} + 2 q^{11} - 24 q^{15} - 34 q^{16} + 60 q^{18} - 44 q^{22} - 4 q^{23} + 70 q^{25} - 40 q^{29} - 50 q^{30} - 86 q^{36} + 18 q^{37} - 70 q^{39} + 32 q^{44} - 100 q^{46} + 30 q^{50} + 50 q^{51} - 42 q^{53} + 60 q^{57} + 8 q^{58} - 82 q^{60} + 60 q^{64} + 24 q^{67} + 108 q^{71} + 20 q^{72} - 90 q^{74} + 28 q^{78} - 60 q^{79} + 42 q^{81} - 150 q^{85} + 88 q^{86} + 66 q^{88} + 74 q^{92} - 56 q^{93} + 100 q^{95} - 196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(539, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
539.2.m.a 539.m 77.l $48$ $4.304$ None \(10\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
539.2.m.b 539.m 77.l $96$ $4.304$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(539, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(539, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)