Properties

Label 675.2.n
Level 675
Weight 2
Character orbit n
Rep. character \(\chi_{675}(109,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 160
Newforms 2
Sturm bound 180
Trace bound 10

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Defining parameters

Level: \( N \) = \( 675 = 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 675.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 2 \)
Sturm bound: \(180\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(675, [\chi])\).

Total New Old
Modular forms 384 160 224
Cusp forms 336 160 176
Eisenstein series 48 0 48

Trace form

\(160q \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(160q \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut 14q^{10} \) \(\mathstrut -\mathstrut 28q^{16} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 14q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut -\mathstrut 120q^{37} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 180q^{49} \) \(\mathstrut +\mathstrut 50q^{52} \) \(\mathstrut +\mathstrut 36q^{55} \) \(\mathstrut +\mathstrut 60q^{58} \) \(\mathstrut +\mathstrut 60q^{61} \) \(\mathstrut +\mathstrut 40q^{64} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut -\mathstrut 156q^{70} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 44q^{79} \) \(\mathstrut -\mathstrut 8q^{85} \) \(\mathstrut -\mathstrut 70q^{88} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 102q^{94} \) \(\mathstrut -\mathstrut 70q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(675, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
675.2.n.a \(80\) \(5.390\) None \(0\) \(0\) \(0\) \(0\)
675.2.n.b \(80\) \(5.390\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(675, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(675, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)