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Properties

Label 138.4.e
Level $138$
Weight $4$
Character orbit 138.e
Rep. character $\chi_{138}(13,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $120$
Newform subspaces $4$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 138.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(138, [\chi])\).

Total New Old
Modular forms 760 120 640
Cusp forms 680 120 560
Eisenstein series 80 0 80

Trace form

\( 120 q - 48 q^{4} - 32 q^{5} + 16 q^{7} - 108 q^{9} + O(q^{10}) \) \( 120 q - 48 q^{4} - 32 q^{5} + 16 q^{7} - 108 q^{9} - 40 q^{10} - 24 q^{11} - 128 q^{13} + 16 q^{14} - 48 q^{15} - 192 q^{16} - 160 q^{17} + 468 q^{19} + 576 q^{20} - 84 q^{21} + 736 q^{22} + 1768 q^{23} + 1420 q^{25} + 664 q^{26} - 288 q^{28} - 1008 q^{29} - 72 q^{30} - 2152 q^{31} + 252 q^{33} - 656 q^{34} - 1772 q^{35} - 432 q^{36} - 936 q^{37} - 416 q^{38} + 108 q^{39} - 160 q^{40} + 1308 q^{41} - 216 q^{42} + 2016 q^{43} - 96 q^{44} - 288 q^{45} + 520 q^{46} + 5184 q^{47} - 1276 q^{49} - 48 q^{50} - 336 q^{51} - 512 q^{52} + 1620 q^{53} - 6004 q^{55} + 64 q^{56} - 3360 q^{57} - 1208 q^{58} - 3788 q^{59} - 192 q^{60} + 252 q^{61} - 1072 q^{62} + 144 q^{63} - 768 q^{64} + 128 q^{65} - 144 q^{66} + 2604 q^{67} + 768 q^{68} + 780 q^{69} + 5792 q^{70} - 456 q^{71} + 680 q^{73} + 1456 q^{74} - 1680 q^{75} + 112 q^{76} - 448 q^{77} + 192 q^{78} - 3164 q^{79} - 512 q^{80} - 972 q^{81} - 3752 q^{82} + 4708 q^{83} - 336 q^{84} - 5828 q^{85} + 2576 q^{86} - 1464 q^{87} - 928 q^{88} + 3212 q^{89} - 360 q^{90} + 6232 q^{91} - 672 q^{92} - 240 q^{93} + 720 q^{94} - 4472 q^{95} - 20 q^{97} - 12880 q^{98} - 5760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(138, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
138.4.e.a 138.e 23.c $30$ $8.142$ None \(-6\) \(-9\) \(-20\) \(-10\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.b 138.e 23.c $30$ $8.142$ None \(-6\) \(9\) \(-6\) \(22\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.c 138.e 23.c $30$ $8.142$ None \(6\) \(-9\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{11}]$
138.4.e.d 138.e 23.c $30$ $8.142$ None \(6\) \(9\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{4}^{\mathrm{old}}(138, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(138, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 2}\)