Properties

Label 45.18.a
Level $45$
Weight $18$
Character orbit 45.a
Rep. character $\chi_{45}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $8$
Sturm bound $108$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 45.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(108\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_0(45))\).

Total New Old
Modular forms 106 29 77
Cusp forms 98 29 69
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
\(+\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(9\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(14\)
Minus space\(-\)\(15\)

Trace form

\( 29 q + 286 q^{2} + 2031680 q^{4} - 390625 q^{5} + 20354440 q^{7} + 204595932 q^{8} + 419531250 q^{10} - 1022680364 q^{11} + 5451754558 q^{13} - 16276829388 q^{14} + 150546980420 q^{16} - 72245108282 q^{17}+ \cdots + 39\!\cdots\!18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_0(45))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5
45.18.a.a 45.a 1.a $2$ $82.450$ \(\Q(\sqrt{39}) \) None 5.18.a.a \(-680\) \(0\) \(781250\) \(-22820700\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-340+\beta )q^{2}+(35072-680\beta )q^{4}+\cdots\)
45.18.a.b 45.a 1.a $2$ $82.450$ \(\Q(\sqrt{849}) \) None 15.18.a.a \(356\) \(0\) \(-781250\) \(-20754552\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(178-\beta )q^{2}+(175688-356\beta )q^{4}+\cdots\)
45.18.a.c 45.a 1.a $3$ $82.450$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 5.18.a.b \(-118\) \(0\) \(-1171875\) \(2139308\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-39+\beta _{1})q^{2}+(5574-14^{2}\beta _{1}+\cdots)q^{4}+\cdots\)
45.18.a.d 45.a 1.a $3$ $82.450$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 15.18.a.c \(253\) \(0\) \(1171875\) \(-4332484\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(84+\beta _{1})q^{2}+(-2408+137\beta _{1}+\cdots)q^{4}+\cdots\)
45.18.a.e 45.a 1.a $3$ $82.450$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None 15.18.a.b \(442\) \(0\) \(1171875\) \(4962644\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(147-\beta _{1})q^{2}+(99318-14^{2}\beta _{1}+\cdots)q^{4}+\cdots\)
45.18.a.f 45.a 1.a $4$ $82.450$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None 15.18.a.d \(33\) \(0\) \(-1562500\) \(17583104\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(8+\beta _{1})q^{2}+(109856-65\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
45.18.a.g 45.a 1.a $6$ $82.450$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 45.18.a.g \(-665\) \(0\) \(-2343750\) \(21788560\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-111+\beta _{1})q^{2}+(71921-112\beta _{1}+\cdots)q^{4}+\cdots\)
45.18.a.h 45.a 1.a $6$ $82.450$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 45.18.a.g \(665\) \(0\) \(2343750\) \(21788560\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(111-\beta _{1})q^{2}+(71921-112\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_0(45))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_0(45)) \simeq \) \(S_{18}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)