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Properties

Label 152.7.s
Level $152$
Weight $7$
Character orbit 152.s
Rep. character $\chi_{152}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $708$
Sturm bound $140$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 152.s (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(140\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(152, [\chi])\).

Total New Old
Modular forms 732 732 0
Cusp forms 708 708 0
Eisenstein series 24 24 0

Trace form

\( 708 q - 6 q^{2} - 204 q^{4} - 492 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9} + O(q^{10}) \) \( 708 q - 6 q^{2} - 204 q^{4} - 492 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9} - 1689 q^{10} - 9 q^{12} - 8229 q^{14} - 12 q^{15} - 1392 q^{16} - 12 q^{17} + 33618 q^{20} - 198 q^{22} - 12 q^{23} + 7116 q^{24} - 12 q^{25} + 84453 q^{26} + 38040 q^{28} - 75516 q^{30} - 18 q^{31} - 158451 q^{32} - 4386 q^{33} + 129252 q^{34} - 414975 q^{36} - 308202 q^{38} - 24 q^{39} + 696300 q^{40} + 31308 q^{41} - 544263 q^{42} - 525639 q^{44} + 807966 q^{46} - 377004 q^{47} - 1606389 q^{48} - 5344632 q^{49} - 793620 q^{50} - 130821 q^{52} - 607095 q^{54} - 93762 q^{55} - 12 q^{57} + 709980 q^{58} - 1612584 q^{60} - 549048 q^{62} + 705882 q^{63} + 524895 q^{64} - 18 q^{65} - 779364 q^{66} - 1125648 q^{68} - 1792047 q^{70} - 12 q^{71} - 3666378 q^{72} + 771108 q^{73} - 2376549 q^{74} - 1467582 q^{76} + 633789 q^{78} - 12 q^{79} + 5129511 q^{80} + 912402 q^{81} + 3214209 q^{82} + 498627 q^{84} - 7453272 q^{86} - 6 q^{87} - 7202529 q^{88} - 12 q^{89} - 9458790 q^{90} + 2545104 q^{92} + 3288468 q^{95} - 2623554 q^{96} - 12 q^{97} + 6362103 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.