Properties

Label 275.2.b
Level $275$
Weight $2$
Character orbit 275.b
Rep. character $\chi_{275}(199,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $5$
Sturm bound $60$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

Total New Old
Modular forms 36 16 20
Cusp forms 24 16 8
Eisenstein series 12 0 12

Trace form

\( 16 q - 10 q^{4} - 16 q^{6} - 14 q^{9} + 4 q^{11} - 4 q^{14} - 10 q^{16} + 12 q^{19} - 16 q^{21} + 20 q^{24} + 16 q^{26} + 8 q^{29} - 2 q^{31} - 12 q^{34} + 22 q^{36} - 4 q^{39} - 8 q^{41} - 2 q^{44} - 24 q^{46}+ \cdots - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
275.2.b.a 275.b 5.b $2$ $2.196$ \(\Q(\sqrt{-1}) \) None 11.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}+2 i q^{7}+\cdots\)
275.2.b.b 275.b 5.b $2$ $2.196$ \(\Q(\sqrt{-1}) \) None 55.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+q^{4}+3 i q^{8}+3 q^{9}-q^{11}+\cdots\)
275.2.b.c 275.b 5.b $4$ $2.196$ \(\Q(i, \sqrt{13})\) None 275.2.a.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
275.2.b.d 275.b 5.b $4$ $2.196$ \(\Q(\zeta_{8})\) None 55.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+(-\beta_{2}+\beta_1)q^{3}+(-\beta_{3}-1)q^{4}+\cdots\)
275.2.b.e 275.b 5.b $4$ $2.196$ \(\Q(i, \sqrt{5})\) None 275.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(275, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)