Properties

Label 76.7.l
Level $76$
Weight $7$
Character orbit 76.l
Rep. character $\chi_{76}(23,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $348$
Newform subspaces $1$
Sturm bound $70$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 76.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(70\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(76, [\chi])\).

Total New Old
Modular forms 372 372 0
Cusp forms 348 348 0
Eisenstein series 24 24 0

Trace form

\( 348q - 6q^{2} + 192q^{4} - 12q^{5} - 492q^{6} - 3q^{8} + 1368q^{9} + O(q^{10}) \) \( 348q - 6q^{2} + 192q^{4} - 12q^{5} - 492q^{6} - 3q^{8} + 1368q^{9} + 2811q^{10} - 3q^{12} - 7572q^{13} + 8217q^{14} - 1392q^{16} - 12q^{17} - 12q^{18} + 33618q^{20} - 33546q^{21} - 198q^{22} - 7128q^{24} - 12q^{25} + 84453q^{26} + 13464q^{28} - 12q^{29} + 75510q^{30} + 9339q^{32} - 366q^{33} - 289248q^{34} - 419349q^{36} - 24q^{37} + 158040q^{38} + 264570q^{40} + 27360q^{41} + 206001q^{42} - 525639q^{44} - 6q^{45} - 269328q^{46} - 703179q^{48} + 2319360q^{49} + 264534q^{50} + 130809q^{52} - 182292q^{53} + 607083q^{54} - 705906q^{56} - 12q^{57} - 710004q^{58} + 1060416q^{60} - 325092q^{61} - 1967868q^{62} - 1611921q^{64} + 398994q^{65} - 2295684q^{66} + 1125642q^{68} - 1625190q^{69} + 3496059q^{70} + 4948626q^{72} - 2224812q^{73} + 2661159q^{74} - 968262q^{76} + 974412q^{77} - 340743q^{78} - 3996663q^{80} + 4277754q^{81} - 3214221q^{82} - 872109q^{84} - 3207900q^{85} + 3189360q^{86} + 827973q^{88} - 2016084q^{89} - 710406q^{90} - 2545116q^{92} + 4486254q^{93} - 14322630q^{94} + 2623530q^{96} - 1223112q^{97} + 10989009q^{98} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.7.l.a \(348\) \(17.484\) None \(-6\) \(0\) \(-12\) \(0\)