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Properties

Label 525.4.bc
Level $525$
Weight $4$
Character orbit 525.bc
Rep. character $\chi_{525}(82,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.bc (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(320\)

Dimensions

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

Total New Old
Modular forms 1008 288 720
Cusp forms 912 288 624
Eisenstein series 96 0 96

Trace form

\( 288 q + 4 q^{7} - 168 q^{8} + O(q^{10}) \) \( 288 q + 4 q^{7} - 168 q^{8} - 112 q^{11} + 2080 q^{16} + 48 q^{21} - 624 q^{22} + 64 q^{23} - 1824 q^{26} - 628 q^{28} + 1056 q^{31} + 672 q^{32} + 108 q^{33} - 10368 q^{36} + 552 q^{37} + 4044 q^{38} + 1068 q^{42} - 720 q^{43} - 680 q^{46} - 240 q^{47} - 672 q^{51} - 4644 q^{52} - 1728 q^{53} - 9792 q^{56} - 1392 q^{57} - 512 q^{58} - 1296 q^{61} + 288 q^{63} + 8208 q^{66} + 3784 q^{67} + 8844 q^{68} + 256 q^{71} + 756 q^{72} + 3312 q^{73} + 6600 q^{77} + 1200 q^{78} + 11664 q^{81} - 6084 q^{82} - 7784 q^{86} - 5652 q^{87} - 4844 q^{88} - 11976 q^{91} + 2152 q^{92} - 1368 q^{93} - 20184 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)