Properties

Label 525.3.be
Level $525$
Weight $3$
Character orbit 525.be
Rep. character $\chi_{525}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $368$
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.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 688 400 288
Cusp forms 592 368 224
Eisenstein series 96 32 64

Trace form

\( 368 q + 6 q^{3} + 16 q^{7} + O(q^{10}) \) \( 368 q + 6 q^{3} + 16 q^{7} + 30 q^{12} + 632 q^{16} - 46 q^{18} + 168 q^{21} + 80 q^{22} + 136 q^{28} - 24 q^{31} + 36 q^{33} + 112 q^{36} - 60 q^{37} - 338 q^{42} + 48 q^{43} - 104 q^{46} - 364 q^{51} + 204 q^{52} - 344 q^{57} + 284 q^{58} + 972 q^{61} - 132 q^{63} - 444 q^{66} + 36 q^{67} + 638 q^{72} - 708 q^{73} - 664 q^{78} - 28 q^{81} - 1104 q^{82} - 246 q^{87} - 180 q^{88} - 372 q^{91} - 196 q^{93} - 3108 q^{96} + O(q^{100}) \)

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

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

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)