Properties

Label 450.2.l
Level 450
Weight 2
Character orbit l
Rep. character \(\chi_{450}(19,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 48
Newforms 4
Sturm bound 180
Trace bound 5

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 450.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 4 \)
Sturm bound: \(180\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(450, [\chi])\).

Total New Old
Modular forms 392 48 344
Cusp forms 328 48 280
Eisenstein series 64 0 64

Trace form

\(48q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(48q \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 44q^{25} \) \(\mathstrut +\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut +\mathstrut 22q^{29} \) \(\mathstrut +\mathstrut 18q^{31} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 14q^{35} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut -\mathstrut 2q^{44} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 70q^{47} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 8q^{50} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut +\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 60q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut -\mathstrut 62q^{65} \) \(\mathstrut -\mathstrut 70q^{67} \) \(\mathstrut -\mathstrut 52q^{70} \) \(\mathstrut +\mathstrut 42q^{71} \) \(\mathstrut -\mathstrut 44q^{74} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 120q^{77} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut -\mathstrut 90q^{83} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut +\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 10q^{92} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 40q^{97} \) \(\mathstrut -\mathstrut 40q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
450.2.l.a \(8\) \(3.593\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
450.2.l.b \(8\) \(3.593\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(10\) \(0\) \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(1-\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{5}+\cdots\)
450.2.l.c \(16\) \(3.593\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{8}q^{2}-\beta _{10}q^{4}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
450.2.l.d \(16\) \(3.593\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(450, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(450, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)