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Properties

Label 175.4.o
Level $175$
Weight $4$
Character orbit 175.o
Rep. character $\chi_{175}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $136$
Newform subspaces $3$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(175, [\chi])\).

Total New Old
Modular forms 264 152 112
Cusp forms 216 136 80
Eisenstein series 48 16 32

Trace form

\( 136 q + 2 q^{2} + 6 q^{3} - 4 q^{7} + 124 q^{8} + 68 q^{11} - 42 q^{12} + 1004 q^{16} + 150 q^{17} - 4 q^{18} - 336 q^{21} + 600 q^{22} - 134 q^{23} + 900 q^{26} + 966 q^{28} - 540 q^{31} - 954 q^{32} - 1062 q^{33}+ \cdots + 7782 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.4.o.a 175.o 35.k $32$ $10.325$ None 175.4.o.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
175.4.o.b 175.o 35.k $40$ $10.325$ None 35.4.k.a \(2\) \(6\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{12}]$
175.4.o.c 175.o 35.k $64$ $10.325$ None 175.4.o.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{4}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)