Properties

Label 605.2.b
Level $605$
Weight $2$
Character orbit 605.b
Rep. character $\chi_{605}(364,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $8$
Sturm bound $132$
Trace bound $6$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(132\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

Total New Old
Modular forms 78 64 14
Cusp forms 54 46 8
Eisenstein series 24 18 6

Trace form

\( 46q - 34q^{4} + 2q^{5} - 8q^{6} - 26q^{9} + O(q^{10}) \) \( 46q - 34q^{4} + 2q^{5} - 8q^{6} - 26q^{9} + 10q^{10} - 16q^{14} + 2q^{15} + 10q^{16} + 16q^{19} + 16q^{20} - 12q^{21} - 4q^{24} + 2q^{25} + 44q^{26} + 12q^{29} + 6q^{30} - 8q^{31} - 40q^{34} - 18q^{35} + 22q^{36} - 28q^{40} - 12q^{41} - 36q^{45} + 8q^{46} + 30q^{49} + 18q^{50} + 28q^{51} - 20q^{54} + 52q^{56} - 24q^{59} - 40q^{60} - 20q^{61} + 38q^{64} - 4q^{69} - 8q^{70} + 24q^{71} - 12q^{74} + 26q^{75} - 24q^{76} + 28q^{79} - 56q^{80} - 18q^{81} - 48q^{84} - 2q^{85} - 4q^{86} - 36q^{89} + 28q^{90} - 8q^{91} + 44q^{94} - 12q^{95} - 36q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
605.2.b.a \(2\) \(4.831\) \(\Q(\sqrt{-11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(3\) \(0\) \(q+(-1+2\beta )q^{3}+2q^{4}+(1+\beta )q^{5}+\cdots\)
605.2.b.b \(4\) \(4.831\) 4.0.4400.1 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(-2-\beta _{3})q^{4}+\beta _{3}q^{5}-\beta _{1}q^{7}+\cdots\)
605.2.b.c \(4\) \(4.831\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
605.2.b.d \(4\) \(4.831\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.e \(4\) \(4.831\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.b.f \(8\) \(4.831\) 8.0.1480160000.1 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.g \(8\) \(4.831\) 8.0.1480160000.1 None \(0\) \(0\) \(4\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
605.2.b.h \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{9}q^{2}-\beta _{8}q^{3}+(-2-\beta _{6})q^{4}+\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)