Properties

Label 435.2.f
Level $435$
Weight $2$
Character orbit 435.f
Rep. character $\chi_{435}(289,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $6$
Sturm bound $120$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 435.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(120\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(435, [\chi])\).

Total New Old
Modular forms 64 32 32
Cusp forms 56 32 24
Eisenstein series 8 0 8

Trace form

\( 32 q + 36 q^{4} - 8 q^{5} - 4 q^{6} + 32 q^{9} + O(q^{10}) \) \( 32 q + 36 q^{4} - 8 q^{5} - 4 q^{6} + 32 q^{9} + 44 q^{16} - 20 q^{20} - 12 q^{24} + 24 q^{25} - 12 q^{29} - 16 q^{30} - 32 q^{34} - 4 q^{35} + 36 q^{36} - 8 q^{45} - 32 q^{49} - 16 q^{51} - 4 q^{54} - 40 q^{59} - 12 q^{64} + 4 q^{65} + 8 q^{71} - 40 q^{74} - 72 q^{80} + 32 q^{81} - 40 q^{86} - 16 q^{91} - 88 q^{94} - 28 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(435, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
435.2.f.a 435.f 145.d $2$ $3.473$ \(\Q(\sqrt{-1}) \) None 435.2.f.a \(-4\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}+q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\)
435.2.f.b 435.f 145.d $2$ $3.473$ \(\Q(\sqrt{-1}) \) None 435.2.f.b \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\)
435.2.f.c 435.f 145.d $2$ $3.473$ \(\Q(\sqrt{-1}) \) None 435.2.f.b \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{3}-q^{4}+(-1+i)q^{5}+q^{6}+\cdots\)
435.2.f.d 435.f 145.d $2$ $3.473$ \(\Q(\sqrt{-1}) \) None 435.2.f.a \(4\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}-q^{3}+2q^{4}+(2+i)q^{5}-2q^{6}+\cdots\)
435.2.f.e 435.f 145.d $12$ $3.473$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 435.2.f.e \(0\) \(-12\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
435.2.f.f 435.f 145.d $12$ $3.473$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 435.2.f.e \(0\) \(12\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(435, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(435, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)