Properties

Label 45.4.a
Level $45$
Weight $4$
Character orbit 45.a
Rep. character $\chi_{45}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $5$
Sturm bound $24$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(24\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(45))\).

Total New Old
Modular forms 22 5 17
Cusp forms 14 5 9
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\( 5q + 36q^{4} + 5q^{5} - 58q^{7} + 36q^{8} + O(q^{10}) \) \( 5q + 36q^{4} + 5q^{5} - 58q^{7} + 36q^{8} - 40q^{10} - 60q^{11} + 18q^{13} - 12q^{14} + 84q^{16} - 66q^{17} - 132q^{19} + 80q^{20} + 352q^{22} + 366q^{23} + 125q^{25} - 396q^{26} - 784q^{28} - 102q^{29} + 20q^{31} - 372q^{32} - 56q^{34} + 250q^{35} + 82q^{37} + 792q^{38} - 420q^{40} - 474q^{41} + 906q^{43} + 132q^{44} + 984q^{46} + 282q^{47} + 1097q^{49} - 1064q^{52} - 114q^{53} - 280q^{55} + 60q^{56} - 304q^{58} - 624q^{59} - 1134q^{61} - 744q^{62} - 820q^{64} + 70q^{65} - 514q^{67} - 360q^{68} + 1200q^{70} + 204q^{71} - 2166q^{73} + 1308q^{74} - 680q^{76} + 1536q^{77} - 1192q^{79} - 880q^{80} + 5024q^{82} - 1650q^{83} - 370q^{85} + 1680q^{86} + 4224q^{88} - 1206q^{89} + 1924q^{91} - 432q^{92} - 560q^{94} - 20q^{95} - 2294q^{97} - 1632q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(45))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5
45.4.a.a \(1\) \(2.655\) \(\Q\) None \(-5\) \(0\) \(5\) \(-30\) \(+\) \(-\) \(q-5q^{2}+17q^{4}+5q^{5}-30q^{7}-45q^{8}+\cdots\)
45.4.a.b \(1\) \(2.655\) \(\Q\) None \(-3\) \(0\) \(5\) \(20\) \(-\) \(-\) \(q-3q^{2}+q^{4}+5q^{5}+20q^{7}+21q^{8}+\cdots\)
45.4.a.c \(1\) \(2.655\) \(\Q\) None \(-1\) \(0\) \(-5\) \(-24\) \(-\) \(+\) \(q-q^{2}-7q^{4}-5q^{5}-24q^{7}+15q^{8}+\cdots\)
45.4.a.d \(1\) \(2.655\) \(\Q\) None \(4\) \(0\) \(5\) \(6\) \(-\) \(-\) \(q+4q^{2}+8q^{4}+5q^{5}+6q^{7}+20q^{10}+\cdots\)
45.4.a.e \(1\) \(2.655\) \(\Q\) None \(5\) \(0\) \(-5\) \(-30\) \(+\) \(+\) \(q+5q^{2}+17q^{4}-5q^{5}-30q^{7}+45q^{8}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(45))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(45)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)