Properties

Label 605.2.m
Level $605$
Weight $2$
Character orbit 605.m
Rep. character $\chi_{605}(112,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $368$
Newform subspaces $7$
Sturm bound $132$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.m (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 7 \)
Sturm bound: \(132\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 624 496 128
Cusp forms 432 368 64
Eisenstein series 192 128 64

Trace form

\( 368q + 10q^{2} + 2q^{3} + 2q^{5} + 20q^{6} + 10q^{8} + O(q^{10}) \) \( 368q + 10q^{2} + 2q^{3} + 2q^{5} + 20q^{6} + 10q^{8} - 124q^{12} + 10q^{13} - 22q^{15} + 40q^{16} + 10q^{18} - 24q^{20} - 64q^{23} - 10q^{25} - 28q^{26} + 14q^{27} - 50q^{28} - 30q^{30} + 28q^{31} + 10q^{35} - 24q^{36} + 14q^{37} - 10q^{38} + 50q^{40} - 40q^{41} - 50q^{42} - 28q^{45} - 60q^{46} + 20q^{47} + 114q^{48} + 50q^{50} - 20q^{51} + 50q^{52} + 44q^{53} - 48q^{56} - 30q^{57} + 26q^{58} - 122q^{60} + 60q^{61} - 100q^{62} + 30q^{63} - 112q^{67} + 30q^{68} - 46q^{70} - 28q^{71} - 80q^{72} - 50q^{73} - 42q^{75} - 236q^{78} + 22q^{80} - 68q^{81} + 14q^{82} - 90q^{83} - 30q^{85} - 108q^{86} + 20q^{90} - 4q^{91} + 40q^{92} + 26q^{93} + 40q^{95} + 14q^{97} + O(q^{100}) \)

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.m.a \(16\) \(4.831\) 16.0.\(\cdots\).1 \(\Q(\sqrt{-11}) \) \(0\) \(2\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{4}+\beta _{5})q^{3}+(-2\beta _{5}-2\beta _{7}+\cdots)q^{4}+\cdots\)
605.2.m.b \(16\) \(4.831\) \(\Q(\zeta_{40})\) None \(0\) \(4\) \(8\) \(0\) \(q+(\zeta_{40}^{9}+\zeta_{40}^{11}+\zeta_{40}^{12}+\zeta_{40}^{15})q^{2}+\cdots\)
605.2.m.c \(32\) \(4.831\) None \(0\) \(6\) \(-2\) \(-20\)
605.2.m.d \(32\) \(4.831\) None \(0\) \(6\) \(-2\) \(20\)
605.2.m.e \(32\) \(4.831\) None \(10\) \(-4\) \(-2\) \(0\)
605.2.m.f \(80\) \(4.831\) None \(0\) \(-4\) \(-4\) \(0\)
605.2.m.g \(160\) \(4.831\) None \(0\) \(-8\) \(4\) \(0\)

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

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