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Properties

Label 525.4.bh
Level $525$
Weight $4$
Character orbit 525.bh
Rep. character $\chi_{525}(13,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $960$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 525.bh (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(525, [\chi])\).

Total New Old
Modular forms 1952 960 992
Cusp forms 1888 960 928
Eisenstein series 64 0 64

Trace form

\( 960 q - 4 q^{7} + 168 q^{8} + O(q^{10}) \) \( 960 q - 4 q^{7} + 168 q^{8} - 168 q^{15} + 3840 q^{16} + 912 q^{22} + 480 q^{23} - 520 q^{25} - 1772 q^{28} + 160 q^{29} - 192 q^{30} + 1344 q^{32} + 1328 q^{35} + 8640 q^{36} + 456 q^{37} - 1068 q^{42} + 928 q^{43} + 14112 q^{50} - 4192 q^{53} - 696 q^{57} - 3016 q^{58} - 840 q^{60} + 36 q^{63} - 19320 q^{64} + 4720 q^{65} + 4784 q^{67} + 2100 q^{70} + 1512 q^{72} - 2352 q^{77} - 1416 q^{78} + 19440 q^{81} - 11280 q^{84} + 472 q^{85} - 6088 q^{88} - 10600 q^{92} - 5472 q^{93} + 19552 q^{95} + 31048 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)