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Properties

Label 175.2.k
Level $175$
Weight $2$
Character orbit 175.k
Rep. character $\chi_{175}(74,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.k (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 52 28 24
Cusp forms 28 20 8
Eisenstein series 24 8 16

Trace form

\( 20 q + 10 q^{4} - 16 q^{6} + 8 q^{9} - 4 q^{11} - 26 q^{14} - 2 q^{16} - 8 q^{19} + 6 q^{21} - 16 q^{24} - 6 q^{26} + 40 q^{29} + 14 q^{31} - 4 q^{36} + 32 q^{39} - 44 q^{41} - 12 q^{44} + 16 q^{46} - 44 q^{49}+ \cdots - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.2.k.a 175.k 35.j $8$ $1.397$ \(\Q(\zeta_{24})\) None 35.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta_{3} q^{2}-\beta_{4} q^{3}+(-\beta_{6}-\beta_1+1)q^{4}+\cdots\)
175.2.k.b 175.k 35.j $12$ $1.397$ 12.0.\(\cdots\).1 None 175.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(\beta _{10}-\beta _{11})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)

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

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