Properties

Label 135.4.e
Level $135$
Weight $4$
Character orbit 135.e
Rep. character $\chi_{135}(46,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 120 24 96
Cusp forms 96 24 72
Eisenstein series 24 0 24

Trace form

\( 24 q - 4 q^{2} - 48 q^{4} - 10 q^{5} + 12 q^{7} + 108 q^{8} + O(q^{10}) \) \( 24 q - 4 q^{2} - 48 q^{4} - 10 q^{5} + 12 q^{7} + 108 q^{8} - 46 q^{11} - 24 q^{13} + 6 q^{14} - 192 q^{16} + 500 q^{17} + 300 q^{19} - 120 q^{20} - 36 q^{22} - 192 q^{23} - 300 q^{25} - 1432 q^{26} - 384 q^{28} + 286 q^{29} + 120 q^{31} + 484 q^{32} + 378 q^{34} + 560 q^{35} + 336 q^{37} - 88 q^{38} + 90 q^{40} + 472 q^{41} + 174 q^{43} - 1652 q^{44} + 540 q^{46} - 400 q^{47} - 1026 q^{49} - 100 q^{50} - 1302 q^{52} + 2024 q^{53} + 1530 q^{56} - 594 q^{58} - 298 q^{59} + 858 q^{61} + 1644 q^{62} + 2760 q^{64} - 840 q^{65} + 1362 q^{67} - 2732 q^{68} + 180 q^{70} - 272 q^{71} + 1812 q^{73} + 1480 q^{74} - 2598 q^{76} - 1056 q^{77} - 888 q^{79} + 4560 q^{80} - 3492 q^{82} - 2508 q^{83} - 360 q^{85} + 2762 q^{86} - 432 q^{88} - 7404 q^{89} + 3984 q^{91} - 4140 q^{92} + 1962 q^{94} - 2040 q^{95} - 474 q^{97} - 2696 q^{98} + O(q^{100}) \)

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.e.a 135.e 9.c $4$ $7.965$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-1\) \(0\) \(10\) \(-9\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+\cdots\)
135.4.e.b 135.e 9.c $6$ $7.965$ 6.0.15759792.1 None \(-1\) \(0\) \(15\) \(43\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{4})q^{2}+(-\beta _{2}+3\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
135.4.e.c 135.e 9.c $14$ $7.965$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(0\) \(-35\) \(-22\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2})q^{2}+(-5-\beta _{3}-5\beta _{5}-\beta _{10}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(135, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(135, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)