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Properties

Label 1872.4.hp
Level $1872$
Weight $4$
Character orbit 1872.hp
Rep. character $\chi_{1872}(163,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1672$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.hp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 208 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 4064 1688 2376
Cusp forms 4000 1672 2328
Eisenstein series 64 16 48

Trace form

\( 1672 q + 4 q^{2} - 6 q^{4} + 8 q^{5} - 8 q^{7} + 10 q^{8} + O(q^{10}) \) \( 1672 q + 4 q^{2} - 6 q^{4} + 8 q^{5} - 8 q^{7} + 10 q^{8} - 94 q^{10} + 2 q^{11} - 4 q^{13} - 200 q^{14} + 166 q^{16} + 12 q^{17} - 2 q^{19} + 150 q^{20} + 214 q^{22} + 12 q^{23} + 41000 q^{25} - 436 q^{26} - 476 q^{28} + 2 q^{29} - 716 q^{32} + 802 q^{34} + 752 q^{35} - 6 q^{37} + 1388 q^{38} + 1552 q^{40} - 438 q^{43} + 1184 q^{44} - 1510 q^{46} - 12 q^{49} + 1774 q^{50} - 718 q^{52} + 8 q^{53} - 292 q^{55} - 644 q^{56} - 2018 q^{58} - 2726 q^{59} - 2 q^{61} - 2928 q^{62} - 3192 q^{64} + 8 q^{65} - 2 q^{67} - 258 q^{68} + 1896 q^{70} + 232 q^{71} + 296 q^{73} - 5322 q^{74} + 4956 q^{76} - 1372 q^{77} + 4500 q^{80} - 328 q^{82} - 2672 q^{83} - 756 q^{85} + 5708 q^{86} + 3080 q^{88} - 88 q^{89} + 786 q^{91} + 960 q^{92} - 7140 q^{94} + 500 q^{95} - 8 q^{97} - 9064 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)