Properties

Label 245.2.e
Level $245$
Weight $2$
Character orbit 245.e
Rep. character $\chi_{245}(116,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $9$
Sturm bound $56$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(56\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 72 28 44
Cusp forms 40 28 12
Eisenstein series 32 0 32

Trace form

\( 28q + 4q^{2} + 2q^{3} - 12q^{4} + 2q^{5} + 4q^{6} - 24q^{8} - 14q^{9} + O(q^{10}) \) \( 28q + 4q^{2} + 2q^{3} - 12q^{4} + 2q^{5} + 4q^{6} - 24q^{8} - 14q^{9} + 2q^{10} + 10q^{11} - 6q^{12} + 8q^{13} - 8q^{15} + 4q^{16} + 4q^{17} + 2q^{18} - 4q^{20} - 16q^{22} + 2q^{23} + 2q^{24} - 14q^{25} - 12q^{26} - 4q^{27} - 16q^{29} - 2q^{30} - 12q^{31} + 8q^{32} + 12q^{33} - 24q^{34} + 28q^{36} - 20q^{37} + 8q^{38} - 14q^{39} + 6q^{40} + 20q^{41} + 12q^{43} + 8q^{44} + 22q^{46} + 4q^{47} - 12q^{48} - 8q^{50} + 22q^{51} - 20q^{52} + 8q^{53} + 6q^{54} - 8q^{55} + 56q^{57} + 18q^{58} - 8q^{59} + 2q^{60} - 6q^{61} + 24q^{62} - 2q^{65} - 4q^{66} + 22q^{67} + 20q^{68} + 12q^{69} - 32q^{71} + 50q^{72} + 4q^{73} + 36q^{74} + 2q^{75} - 32q^{76} - 112q^{78} + 26q^{79} + 6q^{80} + 14q^{81} - 18q^{82} - 4q^{83} - 20q^{85} - 54q^{86} - 2q^{87} - 44q^{88} - 6q^{89} + 16q^{90} + 76q^{92} - 16q^{93} + 4q^{94} + 4q^{95} - 10q^{96} - 24q^{97} + 56q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
245.2.e.a \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
245.2.e.b \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(0\) \(q+(1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
245.2.e.c \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(1\) \(0\) \(q+2\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.d \(2\) \(1.956\) \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(-1\) \(0\) \(q+2\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
245.2.e.e \(4\) \(1.956\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(2\) \(0\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
245.2.e.f \(4\) \(1.956\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-1+\cdots)q^{5}+\cdots\)
245.2.e.g \(4\) \(1.956\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
245.2.e.h \(4\) \(1.956\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(-1\) \(2\) \(0\) \(q+\beta _{1}q^{2}+(-1-\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\cdots\)
245.2.e.i \(4\) \(1.956\) \(\Q(\sqrt{-3}, \sqrt{17})\) None \(1\) \(1\) \(-2\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)