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Properties

Label 525.3.bj
Level $525$
Weight $3$
Character orbit 525.bj
Rep. character $\chi_{525}(62,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1248$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.bj (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

Total New Old
Modular forms 1312 1312 0
Cusp forms 1248 1248 0
Eisenstein series 64 64 0

Trace form

\( 1248 q - 40 q^{4} - 24 q^{7} - 20 q^{9} + O(q^{10}) \) \( 1248 q - 40 q^{4} - 24 q^{7} - 20 q^{9} - 28 q^{15} + 1128 q^{16} + 32 q^{18} - 6 q^{21} - 64 q^{22} + 144 q^{28} + 200 q^{30} - 140 q^{36} + 32 q^{37} - 420 q^{39} - 170 q^{42} - 64 q^{43} - 24 q^{46} - 32 q^{51} - 800 q^{57} + 600 q^{58} + 560 q^{60} - 464 q^{63} - 40 q^{64} + 32 q^{67} - 264 q^{70} - 292 q^{72} - 340 q^{78} - 40 q^{79} - 12 q^{81} + 1190 q^{84} - 136 q^{85} - 64 q^{88} - 12 q^{91} - 568 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

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