Properties

Label 175.10.b
Level $175$
Weight $10$
Character orbit 175.b
Rep. character $\chi_{175}(99,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $9$
Sturm bound $200$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 175.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(200\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(175, [\chi])\).

Total New Old
Modular forms 186 82 104
Cusp forms 174 82 92
Eisenstein series 12 0 12

Trace form

\( 82 q - 22872 q^{4} - 12312 q^{6} - 522294 q^{9} + O(q^{10}) \) \( 82 q - 22872 q^{4} - 12312 q^{6} - 522294 q^{9} + 147952 q^{11} - 153664 q^{14} + 8850568 q^{16} - 1861344 q^{19} + 739508 q^{21} + 8296876 q^{24} + 16305324 q^{26} - 1301356 q^{29} - 18049896 q^{31} + 34344344 q^{34} + 75013092 q^{36} - 59831696 q^{39} + 46753160 q^{41} + 131466630 q^{44} - 120337654 q^{46} - 472713682 q^{49} + 146040476 q^{51} + 724921252 q^{54} + 96246486 q^{56} + 356269412 q^{59} + 143787416 q^{61} - 2222716926 q^{64} - 1426012396 q^{66} - 1808650968 q^{69} + 611907964 q^{71} + 831359154 q^{74} - 1433005284 q^{76} - 1303654700 q^{79} + 3447882298 q^{81} - 558107648 q^{84} + 1054172358 q^{86} + 1482306264 q^{89} + 1407946400 q^{91} + 819507428 q^{94} - 2829797556 q^{96} - 6788024404 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(175, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
175.10.b.a 175.b 5.b $2$ $90.131$ \(\Q(\sqrt{-1}) \) None 35.10.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+28iq^{2}+116iq^{3}-272q^{4}-3248q^{6}+\cdots\)
175.10.b.b 175.b 5.b $4$ $90.131$ \(\Q(i, \sqrt{193})\) None 7.10.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3\beta _{1}+\beta _{2})q^{2}+(43\beta _{1}+11\beta _{2}+\cdots)q^{3}+\cdots\)
175.10.b.c 175.b 5.b $4$ $90.131$ \(\Q(\zeta_{8})\) None 35.10.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(12\zeta_{8}-\zeta_{8}^{2})q^{2}+(-87\zeta_{8}+54\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
175.10.b.d 175.b 5.b $6$ $90.131$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 7.10.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-7\beta _{1}-\beta _{4})q^{2}+(28\beta _{1}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
175.10.b.e 175.b 5.b $8$ $90.131$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 35.10.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(5\beta _{4}-\beta _{5})q^{2}+(-4\beta _{4}+\beta _{6})q^{3}+\cdots\)
175.10.b.f 175.b 5.b $10$ $90.131$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 35.10.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(-28\beta _{1}+\beta _{2})q^{3}+(-168+\cdots)q^{4}+\cdots\)
175.10.b.g 175.b 5.b $12$ $90.131$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 35.10.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+2\beta _{7})q^{2}+(-\beta _{1}+21\beta _{7}+\beta _{8}+\cdots)q^{3}+\cdots\)
175.10.b.h 175.b 5.b $16$ $90.131$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 175.10.a.h \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-3\beta _{9})q^{2}+(\beta _{1}-8\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
175.10.b.i 175.b 5.b $20$ $90.131$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None 175.10.a.j \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2\beta _{10}+\beta _{11})q^{2}+(8\beta _{10}-\beta _{13})q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(175, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(175, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)