Properties

Label 435.2.a
Level $435$
Weight $2$
Character orbit 435.a
Rep. character $\chi_{435}(1,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $10$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 435.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(435))\).

Total New Old
Modular forms 64 19 45
Cusp forms 57 19 38
Eisenstein series 7 0 7

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

\(3\)\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(6\)
Minus space\(-\)\(13\)

Trace form

\( 19 q - 3 q^{2} + 3 q^{3} + 21 q^{4} - q^{5} + q^{6} - 15 q^{8} + 19 q^{9} + O(q^{10}) \) \( 19 q - 3 q^{2} + 3 q^{3} + 21 q^{4} - q^{5} + q^{6} - 15 q^{8} + 19 q^{9} + 5 q^{10} + 4 q^{11} + 5 q^{12} + 10 q^{13} + 3 q^{15} + 29 q^{16} - 10 q^{17} - 3 q^{18} + 4 q^{19} + 9 q^{20} + 8 q^{21} - 24 q^{22} - 16 q^{23} + 9 q^{24} + 19 q^{25} - 18 q^{26} + 3 q^{27} - 20 q^{28} - q^{29} - 3 q^{30} - 8 q^{31} - 23 q^{32} - 12 q^{33} + 22 q^{34} + 21 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} + 9 q^{40} + 14 q^{41} - 12 q^{42} - 4 q^{43} + 28 q^{44} - q^{45} - 40 q^{46} - 8 q^{47} - 3 q^{48} + 35 q^{49} - 3 q^{50} - 2 q^{51} + 26 q^{52} - 22 q^{53} + q^{54} + 12 q^{55} - 48 q^{56} + 20 q^{57} + q^{58} + 28 q^{59} + 5 q^{60} - 6 q^{61} + 16 q^{62} + 41 q^{64} + 18 q^{65} - 36 q^{66} - 36 q^{67} - 46 q^{68} - 8 q^{71} - 15 q^{72} - 10 q^{73} + 38 q^{74} + 3 q^{75} - 68 q^{76} - 40 q^{77} - 30 q^{78} + 32 q^{79} + q^{80} + 19 q^{81} + 2 q^{82} - 36 q^{83} + 32 q^{84} + 6 q^{85} - 68 q^{86} + 11 q^{87} - 68 q^{88} + 14 q^{89} + 5 q^{90} - 16 q^{92} + 8 q^{93} + 28 q^{94} - 4 q^{95} - 11 q^{96} + 6 q^{97} - 35 q^{98} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(435))\) 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 29
435.2.a.a 435.a 1.a $1$ $3.473$ \(\Q\) None 435.2.a.a \(-1\) \(1\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}-4q^{7}+\cdots\)
435.2.a.b 435.a 1.a $1$ $3.473$ \(\Q\) None 435.2.a.b \(0\) \(-1\) \(-1\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+q^{11}+\cdots\)
435.2.a.c 435.a 1.a $1$ $3.473$ \(\Q\) None 435.2.a.c \(0\) \(1\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}+2q^{7}+q^{9}+3q^{11}+\cdots\)
435.2.a.d 435.a 1.a $1$ $3.473$ \(\Q\) None 435.2.a.d \(1\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+4q^{7}+\cdots\)
435.2.a.e 435.a 1.a $2$ $3.473$ \(\Q(\sqrt{5}) \) None 435.2.a.e \(-1\) \(2\) \(-2\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
435.2.a.f 435.a 1.a $2$ $3.473$ \(\Q(\sqrt{21}) \) None 435.2.a.f \(-1\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(3+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
435.2.a.g 435.a 1.a $2$ $3.473$ \(\Q(\sqrt{5}) \) None 435.2.a.g \(0\) \(2\) \(-2\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}-q^{5}-\beta q^{6}+2q^{7}+\cdots\)
435.2.a.h 435.a 1.a $2$ $3.473$ \(\Q(\sqrt{17}) \) None 435.2.a.h \(1\) \(2\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
435.2.a.i 435.a 1.a $3$ $3.473$ 3.3.469.1 None 435.2.a.i \(1\) \(-3\) \(3\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
435.2.a.j 435.a 1.a $4$ $3.473$ 4.4.2225.1 None 435.2.a.j \(-3\) \(-4\) \(-4\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(435))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(435)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)