↑

Properties

Label 1148.4.bh
Level $1148$
Weight $4$
Character orbit 1148.bh
Rep. character $\chi_{1148}(255,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2000$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1148.bh (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1148 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1148, [\chi])\).

Total New Old
Modular forms 2032 2032 0
Cusp forms 2000 2000 0
Eisenstein series 32 32 0

Trace form

\( 2000 q - 4 q^{4} + O(q^{10}) \) \( 2000 q - 4 q^{4} - 12 q^{10} - 6 q^{12} + 78 q^{14} - 4 q^{16} - 12 q^{17} - 68 q^{18} - 480 q^{22} + 372 q^{24} - 24208 q^{25} - 804 q^{26} - 296 q^{28} - 128 q^{29} - 740 q^{30} - 8 q^{37} - 3240 q^{38} + 1488 q^{40} - 1360 q^{42} - 258 q^{44} - 24 q^{45} + 2862 q^{52} - 4 q^{53} + 3198 q^{54} + 2630 q^{56} - 32 q^{57} + 700 q^{58} - 1940 q^{60} - 3880 q^{64} - 784 q^{65} + 6588 q^{66} - 7458 q^{68} - 4594 q^{70} + 7812 q^{72} + 3240 q^{78} + 69648 q^{81} + 5778 q^{82} - 1608 q^{85} - 36 q^{86} - 2692 q^{88} + 6348 q^{89} - 6464 q^{92} - 700 q^{93} + 4368 q^{94} - 13878 q^{96} - 196 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1148, [\chi])\) into newform subspaces

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