Properties

Label 450.2.h
Level $450$
Weight $2$
Character orbit 450.h
Rep. character $\chi_{450}(91,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $52$
Newform subspaces $7$
Sturm bound $180$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
Sturm bound: \(180\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 392 52 340
Cusp forms 328 52 276
Eisenstein series 64 0 64

Trace form

\( 52q - q^{2} - 13q^{4} - 11q^{5} - q^{8} + O(q^{10}) \) \( 52q - q^{2} - 13q^{4} - 11q^{5} - q^{8} + q^{10} + 8q^{11} + 6q^{13} + 4q^{14} - 13q^{16} + 16q^{17} - 14q^{19} + 4q^{20} - 8q^{22} + 30q^{23} + 7q^{25} - 30q^{26} - 10q^{28} + 12q^{29} - 18q^{31} + 4q^{32} + 5q^{34} + 14q^{35} - 13q^{37} + 4q^{38} + q^{40} + 20q^{41} + 28q^{43} - 2q^{44} - 16q^{46} - 30q^{47} + 68q^{49} - q^{50} + 6q^{52} + 39q^{53} + 38q^{55} + 4q^{56} - 18q^{58} - 40q^{61} - 8q^{62} - 13q^{64} - 47q^{65} + 2q^{67} - 54q^{68} - 12q^{70} - 2q^{71} - 62q^{73} - 54q^{74} + 16q^{76} - 40q^{77} - 40q^{79} - q^{80} - 86q^{82} - 18q^{83} + 13q^{85} - 2q^{86} + 2q^{88} - q^{89} - 36q^{91} - 30q^{92} + 8q^{94} + 44q^{95} + 14q^{97} + 31q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(450, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
450.2.h.a \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(-12\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.b \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(8\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.c \(4\) \(3.593\) \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-5\) \(6\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
450.2.h.d \(8\) \(3.593\) 8.0.1064390625.3 None \(-2\) \(0\) \(4\) \(-2\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots\)
450.2.h.e \(8\) \(3.593\) 8.0.58140625.2 None \(2\) \(0\) \(0\) \(4\) \(q+\beta _{6}q^{2}-\beta _{3}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
450.2.h.f \(12\) \(3.593\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(1\) \(-2\) \(q-\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)
450.2.h.g \(12\) \(3.593\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(-1\) \(-2\) \(q+\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)

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

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