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Properties

Label 1872.4.ba
Level $1872$
Weight $4$
Character orbit 1872.ba
Rep. character $\chi_{1872}(469,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $720$
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.ba (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 2032 720 1312
Cusp forms 2000 720 1280
Eisenstein series 32 0 32

Trace form

\( 720 q - 20 q^{4} + 84 q^{8} + O(q^{10}) \) \( 720 q - 20 q^{4} + 84 q^{8} - 108 q^{10} - 40 q^{11} - 140 q^{14} + 204 q^{16} - 48 q^{19} - 308 q^{20} + 20 q^{22} + 400 q^{29} - 744 q^{31} + 980 q^{32} + 408 q^{34} - 456 q^{35} + 16 q^{37} - 168 q^{38} - 288 q^{40} + 376 q^{43} + 2572 q^{44} - 48 q^{46} - 1880 q^{47} - 35280 q^{49} + 2128 q^{50} + 936 q^{52} + 752 q^{53} + 844 q^{56} - 1088 q^{58} + 1824 q^{61} + 104 q^{62} + 4480 q^{64} - 2256 q^{67} + 968 q^{68} + 828 q^{70} - 840 q^{74} + 2100 q^{76} + 1904 q^{77} - 5664 q^{79} + 772 q^{80} - 2920 q^{82} - 2440 q^{83} + 480 q^{85} + 8280 q^{86} + 280 q^{88} + 9180 q^{92} + 5972 q^{94} - 7728 q^{95} + 10184 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(624, [\chi])\)\(^{\oplus 2}\)