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Properties

Label 381.2.q
Level $381$
Weight $2$
Character orbit 381.q
Rep. character $\chi_{381}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $264$
Newform subspaces $2$
Sturm bound $85$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 381 = 3 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 381.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 127 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 2 \)
Sturm bound: \(85\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(381, [\chi])\).

Total New Old
Modular forms 528 264 264
Cusp forms 480 264 216
Eisenstein series 48 0 48

Trace form

\( 264 q - 10 q^{2} + 2 q^{3} - 58 q^{4} + 2 q^{6} - 8 q^{7} + 28 q^{8} + 22 q^{9} + O(q^{10}) \) \( 264 q - 10 q^{2} + 2 q^{3} - 58 q^{4} + 2 q^{6} - 8 q^{7} + 28 q^{8} + 22 q^{9} + 4 q^{10} - 26 q^{11} - 14 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{15} - 58 q^{16} - 4 q^{17} - 2 q^{18} - 32 q^{19} + 16 q^{20} - 30 q^{21} + 2 q^{22} - 8 q^{23} - 36 q^{24} - 68 q^{25} + 112 q^{26} - 4 q^{27} - 10 q^{28} - 8 q^{29} - 12 q^{30} - 4 q^{31} - 30 q^{32} + 48 q^{33} + 30 q^{34} + 22 q^{36} + 2 q^{37} - 90 q^{38} + 2 q^{39} - 28 q^{40} - 56 q^{41} - 22 q^{42} - 6 q^{43} - 62 q^{44} + 4 q^{46} - 54 q^{47} + 70 q^{48} - 34 q^{49} + 72 q^{50} - 12 q^{51} + 18 q^{52} - 14 q^{53} - 4 q^{54} + 38 q^{55} - 44 q^{56} - 10 q^{57} + 52 q^{58} - 26 q^{59} - 88 q^{60} + 30 q^{61} + 26 q^{62} - 12 q^{63} - 20 q^{64} + 54 q^{65} - 12 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} - 16 q^{70} + 66 q^{71} - 14 q^{72} - 28 q^{73} + 188 q^{74} - 104 q^{75} - 74 q^{76} - 58 q^{77} + 4 q^{78} - 118 q^{79} + 2 q^{80} + 22 q^{81} + 40 q^{82} + 18 q^{83} + 28 q^{84} - 38 q^{85} - 180 q^{86} - 2 q^{88} + 44 q^{89} - 2 q^{90} - 130 q^{91} - 142 q^{92} - 26 q^{93} + 20 q^{94} - 12 q^{95} + 14 q^{96} - 42 q^{97} + 60 q^{98} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(381, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
381.2.q.a 381.q 127.i $120$ $3.042$ None \(-3\) \(-10\) \(2\) \(11\) $\mathrm{SU}(2)[C_{21}]$
381.2.q.b 381.q 127.i $144$ $3.042$ None \(-7\) \(12\) \(-2\) \(-19\) $\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(381, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(381, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(127, [\chi])\)\(^{\oplus 2}\)