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Properties

Label 152.7.l
Level $152$
Weight $7$
Character orbit 152.l
Rep. character $\chi_{152}(69,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $236$
Sturm bound $140$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 244 244 0
Cusp forms 236 236 0
Eisenstein series 8 8 0

Trace form

\( 236 q - 3 q^{2} + 65 q^{4} + 289 q^{6} - 8 q^{7} - 27704 q^{9} + O(q^{10}) \) \( 236 q - 3 q^{2} + 65 q^{4} + 289 q^{6} - 8 q^{7} - 27704 q^{9} + 1680 q^{10} + 8220 q^{14} - 6 q^{15} + 461 q^{16} - 2 q^{17} + 6344 q^{20} + 189 q^{22} - 2 q^{23} - 33907 q^{24} + 343748 q^{25} - 78080 q^{26} + 42946 q^{28} - 208608 q^{30} + 46617 q^{32} + 4368 q^{33} + 184614 q^{34} - 8788 q^{36} + 2952 q^{38} + 2908 q^{39} - 45960 q^{40} - 31326 q^{41} - 74546 q^{42} - 146539 q^{44} + 125662 q^{47} + 442833 q^{48} + 3357156 q^{49} + 130812 q^{52} + 51751 q^{54} + 31248 q^{55} + 15414 q^{57} + 9880 q^{58} - 385614 q^{60} + 865018 q^{62} - 232384 q^{63} + 2379062 q^{64} + 1105203 q^{66} - 325108 q^{68} - 2703462 q^{70} - 6 q^{71} - 1615236 q^{72} - 257042 q^{73} - 68104 q^{74} + 2561775 q^{76} + 3557376 q^{78} - 6 q^{79} - 1627672 q^{80} - 6327138 q^{81} - 274509 q^{82} + 4130328 q^{86} - 2026980 q^{87} - 6 q^{89} + 2757156 q^{90} + 2144446 q^{92} - 3120022 q^{95} + 3549930 q^{96} - 6 q^{97} + 6650943 q^{98} + O(q^{100}) \)

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.