Properties

Label 1575.2.bf
Level 1575
Weight 2
Character orbit bf
Rep. character \(\chi_{1575}(551,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 292
Sturm bound 480

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\(292q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 139q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(292q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 139q^{4} \) \(\mathstrut +\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 3q^{12} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 123q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 2q^{22} \) \(\mathstrut +\mathstrut 12q^{24} \) \(\mathstrut +\mathstrut 18q^{26} \) \(\mathstrut -\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 39q^{32} \) \(\mathstrut +\mathstrut 30q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 60q^{36} \) \(\mathstrut +\mathstrut 3q^{37} \) \(\mathstrut +\mathstrut 66q^{38} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 21q^{42} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 45q^{48} \) \(\mathstrut +\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut 42q^{54} \) \(\mathstrut -\mathstrut 18q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 180q^{64} \) \(\mathstrut +\mathstrut 45q^{66} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 108q^{68} \) \(\mathstrut +\mathstrut 48q^{69} \) \(\mathstrut +\mathstrut 49q^{72} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 48q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 14q^{79} \) \(\mathstrut +\mathstrut 21q^{81} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 69q^{84} \) \(\mathstrut +\mathstrut 63q^{87} \) \(\mathstrut -\mathstrut 22q^{88} \) \(\mathstrut -\mathstrut 27q^{89} \) \(\mathstrut +\mathstrut 5q^{91} \) \(\mathstrut -\mathstrut 42q^{92} \) \(\mathstrut +\mathstrut 48q^{93} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 126q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 33q^{98} \) \(\mathstrut -\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into irreducible Hecke orbits

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

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)