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Properties

Label 175.2.o
Level $175$
Weight $2$
Character orbit 175.o
Rep. character $\chi_{175}(68,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $40$
Newform subspaces $4$
Sturm bound $40$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.o (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(175, [\chi])\).

Total New Old
Modular forms 104 56 48
Cusp forms 56 40 16
Eisenstein series 48 16 32

Trace form

\( 40 q + 2 q^{2} + 6 q^{3} + 10 q^{7} + 4 q^{8} + O(q^{10}) \) \( 40 q + 2 q^{2} + 6 q^{3} + 10 q^{7} + 4 q^{8} - 20 q^{11} - 6 q^{12} - 12 q^{16} - 12 q^{17} - 4 q^{18} - 44 q^{21} - 8 q^{22} - 10 q^{23} + 12 q^{26} - 18 q^{28} + 12 q^{31} + 18 q^{32} - 32 q^{36} + 12 q^{38} + 26 q^{42} + 12 q^{43} - 8 q^{46} - 24 q^{47} + 4 q^{51} - 24 q^{52} - 20 q^{53} - 104 q^{56} - 16 q^{57} + 6 q^{58} + 72 q^{61} + 4 q^{63} + 204 q^{66} + 14 q^{67} + 12 q^{68} - 96 q^{71} + 8 q^{72} + 24 q^{73} + 20 q^{77} - 32 q^{78} - 64 q^{81} + 6 q^{82} - 24 q^{86} - 18 q^{87} + 8 q^{88} + 36 q^{91} + 36 q^{92} - 4 q^{93} + 60 q^{96} - 18 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.o.a 175.o 35.k $4$ $1.397$ \(\Q(\zeta_{12})\) None \(-2\) \(4\) \(0\) \(10\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-1+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
175.2.o.b 175.o 35.k $4$ $1.397$ \(\Q(\zeta_{12})\) None \(4\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1-\zeta_{12})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
175.2.o.c 175.o 35.k $8$ $1.397$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
175.2.o.d 175.o 35.k $24$ $1.397$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

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