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Properties

Label 38.6.c
Level $38$
Weight $6$
Character orbit 38.c
Rep. character $\chi_{38}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $14$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(38, [\chi])\).

Total New Old
Modular forms 54 14 40
Cusp forms 46 14 32
Eisenstein series 8 0 8

Trace form

\( 14 q - 4 q^{2} - 29 q^{3} - 112 q^{4} - 22 q^{5} + 4 q^{6} - 548 q^{7} + 128 q^{8} - 254 q^{9} + O(q^{10}) \) \( 14 q - 4 q^{2} - 29 q^{3} - 112 q^{4} - 22 q^{5} + 4 q^{6} - 548 q^{7} + 128 q^{8} - 254 q^{9} - 200 q^{10} - 794 q^{11} + 928 q^{12} - 1410 q^{13} - 1400 q^{14} + 934 q^{15} - 1792 q^{16} - 478 q^{17} - 4528 q^{18} + 6001 q^{19} + 704 q^{20} + 5046 q^{21} - 2164 q^{22} - 2372 q^{23} + 64 q^{24} - 5345 q^{25} - 496 q^{26} + 29806 q^{27} + 4384 q^{28} - 4226 q^{29} + 7792 q^{30} - 1928 q^{31} - 1024 q^{32} - 12061 q^{33} + 6088 q^{34} - 9180 q^{35} - 4064 q^{36} - 5448 q^{37} + 11088 q^{38} + 81636 q^{39} - 3200 q^{40} - 23031 q^{41} - 26344 q^{42} - 992 q^{43} + 6352 q^{44} - 62848 q^{45} - 15712 q^{46} - 38342 q^{47} - 7424 q^{48} - 482 q^{49} - 8232 q^{50} - 50474 q^{51} - 22560 q^{52} + 42498 q^{53} + 6988 q^{54} + 45110 q^{55} + 44800 q^{56} - 127464 q^{57} + 57584 q^{58} - 84331 q^{59} + 14944 q^{60} + 5662 q^{61} + 5440 q^{62} + 67192 q^{63} + 57344 q^{64} - 153536 q^{65} - 76956 q^{66} + 42791 q^{67} + 15296 q^{68} + 175664 q^{69} + 3216 q^{70} - 47514 q^{71} + 36224 q^{72} - 22337 q^{73} + 91136 q^{74} + 372870 q^{75} - 32144 q^{76} + 379028 q^{77} - 13352 q^{78} + 25988 q^{79} - 5632 q^{80} - 69467 q^{81} + 64284 q^{82} - 283010 q^{83} - 161472 q^{84} - 119340 q^{85} + 36496 q^{86} - 331732 q^{87} + 69248 q^{88} - 304090 q^{89} - 331936 q^{90} + 445300 q^{91} - 37952 q^{92} + 480820 q^{93} + 425552 q^{94} - 18188 q^{95} - 2048 q^{96} - 379003 q^{97} - 6628 q^{98} - 109682 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.6.c.a 38.c 19.c $6$ $6.095$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(12\) \(-15\) \(14\) \(-624\) $\mathrm{SU}(2)[C_{3}]$ \(q+(4-4\beta _{3})q^{2}+(-5+\beta _{1}+\beta _{2}+5\beta _{3}+\cdots)q^{3}+\cdots\)
38.6.c.b 38.c 19.c $8$ $6.095$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-16\) \(-14\) \(-36\) \(76\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\beta _{2})q^{2}+(-3+3\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)