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Properties

Label 1859.4.b
Level $1859$
Weight $4$
Character orbit 1859.b
Rep. character $\chi_{1859}(1013,\cdot)$
Character field $\Q$
Dimension $384$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1859, [\chi])\).

Total New Old
Modular forms 560 384 176
Cusp forms 532 384 148
Eisenstein series 28 0 28

Trace form

\( 384 q - 1528 q^{4} + 3420 q^{9} + O(q^{10}) \) \( 384 q - 1528 q^{4} + 3420 q^{9} + 112 q^{10} + 108 q^{12} - 8 q^{14} + 5992 q^{16} - 276 q^{17} - 44 q^{22} + 384 q^{23} - 9392 q^{25} + 288 q^{27} + 588 q^{29} - 880 q^{30} - 136 q^{35} - 15040 q^{36} - 240 q^{38} + 216 q^{40} - 1220 q^{42} - 768 q^{43} - 1684 q^{48} - 18416 q^{49} + 928 q^{51} - 2704 q^{53} - 440 q^{55} + 2524 q^{56} + 1844 q^{61} - 2544 q^{62} - 24948 q^{64} - 1628 q^{66} + 5064 q^{68} + 3288 q^{69} + 4336 q^{74} + 632 q^{75} + 616 q^{77} - 344 q^{79} + 33168 q^{81} - 2488 q^{82} + 2888 q^{87} - 264 q^{88} + 2488 q^{90} - 724 q^{92} + 728 q^{94} - 1440 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1859, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1859, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 2}\)