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Properties

Label 135.4.q
Level $135$
Weight $4$
Character orbit 135.q
Rep. character $\chi_{135}(2,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $624$
Newform subspaces $1$
Sturm bound $72$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.q (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(72\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(135, [\chi])\).

Total New Old
Modular forms 672 672 0
Cusp forms 624 624 0
Eisenstein series 48 48 0

Trace form

\( 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8} + O(q^{10}) \) \( 624 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} + 702 q^{18} + 756 q^{20} - 24 q^{21} - 12 q^{22} - 324 q^{23} + 420 q^{25} - 900 q^{27} - 24 q^{28} - 1020 q^{30} - 24 q^{31} + 1752 q^{32} + 516 q^{33} + 2466 q^{35} + 984 q^{36} - 6 q^{37} - 132 q^{38} - 396 q^{40} + 1680 q^{41} - 2256 q^{42} - 12 q^{43} - 1332 q^{45} - 12 q^{46} - 3480 q^{47} - 3228 q^{48} - 684 q^{50} - 6840 q^{51} + 84 q^{52} - 24 q^{55} - 4752 q^{56} + 1842 q^{57} - 12 q^{58} - 2376 q^{60} - 132 q^{61} - 18 q^{62} + 2592 q^{63} + 2076 q^{65} + 9864 q^{66} + 3660 q^{67} + 2676 q^{68} - 12 q^{70} - 36 q^{71} + 1908 q^{72} - 6 q^{73} + 9300 q^{75} - 792 q^{76} - 3324 q^{77} - 606 q^{78} - 3336 q^{81} - 24 q^{82} - 2832 q^{83} - 12 q^{85} - 12516 q^{86} - 8640 q^{87} - 3036 q^{88} - 14532 q^{90} - 12 q^{91} - 1938 q^{92} + 6804 q^{93} - 4302 q^{95} + 3732 q^{96} + 6900 q^{97} - 5832 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(135, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
135.4.q.a 135.q 135.q $624$ $7.965$ None \(-12\) \(-12\) \(-12\) \(-12\) $\mathrm{SU}(2)[C_{36}]$