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Properties

Label 48.6.k
Level $48$
Weight $6$
Character orbit 48.k
Rep. character $\chi_{48}(11,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $76$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 48.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(48, [\chi])\).

Total New Old
Modular forms 84 84 0
Cusp forms 76 76 0
Eisenstein series 8 8 0

Trace form

\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} + O(q^{10}) \) \( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.6.k.a 48.k 48.k $76$ $7.698$ None \(0\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$