Properties

Label 245.2.b
Level $245$
Weight $2$
Character orbit 245.b
Rep. character $\chi_{245}(99,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $56$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(56\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(245, [\chi])\).

Total New Old
Modular forms 36 26 10
Cusp forms 20 16 4
Eisenstein series 16 10 6

Trace form

\( 16 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} + O(q^{10}) \) \( 16 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 12 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{15} + 8 q^{16} - 8 q^{20} - 4 q^{25} - 4 q^{26} - 20 q^{29} + 36 q^{30} - 4 q^{31} + 28 q^{34} - 28 q^{36} - 4 q^{41} - 80 q^{44} + 8 q^{45} + 4 q^{46} + 36 q^{50} + 32 q^{51} - 20 q^{54} - 12 q^{55} + 20 q^{59} + 48 q^{60} + 16 q^{61} + 8 q^{64} + 36 q^{65} + 12 q^{66} + 12 q^{69} + 8 q^{71} - 24 q^{74} - 8 q^{75} - 16 q^{79} - 16 q^{80} - 48 q^{81} - 4 q^{85} + 12 q^{86} - 8 q^{90} - 12 q^{94} - 32 q^{95} + 16 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
245.2.b.a 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None 35.2.b.a \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}+iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
245.2.b.b 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None 35.2.j.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}+q^{4}+(-1+2i)q^{5}+\cdots\)
245.2.b.c 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-1}) \) None 35.2.j.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
245.2.b.d 245.b 5.b $2$ $1.956$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-35}) \) 245.2.b.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{3}+2q^{4}+\beta q^{5}-2q^{9}-3q^{11}+\cdots\)
245.2.b.e 245.b 5.b $4$ $1.956$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 245.2.b.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{2}q^{3}-4q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
245.2.b.f 245.b 5.b $4$ $1.956$ \(\Q(\zeta_{8})\) None 245.2.b.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+(2\zeta_{8}+2\zeta_{8}^{3})q^{3}+q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(245, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)