Properties

Label 950.2.h
Level $950$
Weight $2$
Character orbit 950.h
Rep. character $\chi_{950}(191,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $176$
Newform subspaces $5$
Sturm bound $300$
Trace bound $5$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(300\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

Total New Old
Modular forms 616 176 440
Cusp forms 584 176 408
Eisenstein series 32 0 32

Trace form

\( 176q + 2q^{2} + 8q^{3} - 44q^{4} - 12q^{5} + 4q^{6} + 12q^{7} + 2q^{8} - 32q^{9} + O(q^{10}) \) \( 176q + 2q^{2} + 8q^{3} - 44q^{4} - 12q^{5} + 4q^{6} + 12q^{7} + 2q^{8} - 32q^{9} + 10q^{10} - 2q^{11} - 12q^{12} + 12q^{13} + 12q^{15} - 44q^{16} - 2q^{17} - 40q^{18} + 2q^{19} - 2q^{20} + 8q^{22} + 2q^{23} - 16q^{24} - 36q^{25} - 36q^{26} - 4q^{27} - 8q^{28} + 12q^{29} + 12q^{30} + 12q^{31} - 8q^{32} - 44q^{33} - 30q^{34} + 38q^{35} - 32q^{36} + 30q^{37} + 40q^{39} + 10q^{40} - 24q^{41} + 12q^{42} + 20q^{43} + 8q^{44} + 60q^{45} + 36q^{47} - 12q^{48} + 172q^{49} + 10q^{50} + 24q^{51} + 12q^{52} + 18q^{53} + 16q^{54} + 56q^{55} + 60q^{58} - 12q^{59} - 28q^{60} + 36q^{61} - 72q^{62} - 2q^{63} - 44q^{64} + 54q^{65} + 16q^{66} - 4q^{67} + 8q^{68} - 136q^{69} - 112q^{70} + 40q^{71} + 10q^{72} - 8q^{73} - 52q^{74} - 20q^{75} - 8q^{76} + 56q^{77} - 60q^{78} - 16q^{79} + 8q^{80} - 24q^{81} - 92q^{82} - 50q^{83} - 36q^{85} + 24q^{86} + 56q^{87} - 12q^{88} - 38q^{89} + 10q^{90} - 16q^{91} - 8q^{92} + 64q^{93} + 2q^{95} + 4q^{96} + 120q^{97} + 18q^{98} + 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
950.2.h.a \(4\) \(7.586\) \(\Q(\zeta_{10})\) None \(1\) \(4\) \(5\) \(-12\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(2+\cdots)q^{3}+\cdots\)
950.2.h.b \(40\) \(7.586\) None \(-10\) \(5\) \(0\) \(-12\)
950.2.h.c \(44\) \(7.586\) None \(-11\) \(1\) \(-1\) \(18\)
950.2.h.d \(44\) \(7.586\) None \(11\) \(-1\) \(-11\) \(-10\)
950.2.h.e \(44\) \(7.586\) None \(11\) \(-1\) \(-5\) \(28\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)