Properties

Label 1575.2.j
Level 1575
Weight 2
Character orbit j
Rep. character \(\chi_{1575}(226,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 120
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.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 528 132 396
Cusp forms 432 120 312
Eisenstein series 96 12 84

Trace form

\(120q \) \(\mathstrut -\mathstrut 54q^{4} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(120q \) \(\mathstrut -\mathstrut 54q^{4} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut -\mathstrut 42q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 48q^{34} \) \(\mathstrut +\mathstrut 14q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 64q^{44} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 44q^{52} \) \(\mathstrut -\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 36q^{62} \) \(\mathstrut -\mathstrut 16q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 24q^{74} \) \(\mathstrut -\mathstrut 76q^{76} \) \(\mathstrut +\mathstrut 64q^{77} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut +\mathstrut 6q^{86} \) \(\mathstrut +\mathstrut 76q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 76q^{92} \) \(\mathstrut -\mathstrut 54q^{94} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut 10q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)