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Properties

Label 375.2.g
Level $375$
Weight $2$
Character orbit 375.g
Rep. character $\chi_{375}(76,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $56$
Newform subspaces $5$
Sturm bound $100$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(100\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(375, [\chi])\).

Total New Old
Modular forms 240 56 184
Cusp forms 160 56 104
Eisenstein series 80 0 80

Trace form

\( 56 q + 2 q^{2} - 12 q^{4} + 2 q^{6} + 8 q^{7} - 12 q^{8} - 14 q^{9} + O(q^{10}) \) \( 56 q + 2 q^{2} - 12 q^{4} + 2 q^{6} + 8 q^{7} - 12 q^{8} - 14 q^{9} - 6 q^{11} + 8 q^{12} + 12 q^{13} + 12 q^{14} - 20 q^{16} + 10 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 30 q^{22} - 36 q^{23} - 24 q^{24} - 8 q^{26} + 26 q^{28} - 36 q^{29} + 6 q^{31} - 12 q^{32} + 6 q^{33} + 66 q^{34} - 12 q^{36} + 8 q^{37} + 26 q^{38} + 8 q^{39} - 34 q^{41} + 14 q^{42} - 32 q^{43} - 26 q^{44} + 16 q^{46} + 16 q^{47} + 32 q^{48} + 40 q^{49} - 32 q^{51} - 40 q^{52} - 36 q^{53} + 2 q^{54} + 16 q^{57} - 38 q^{58} - 12 q^{59} - 20 q^{61} - 14 q^{62} - 2 q^{63} - 18 q^{64} + 16 q^{66} + 124 q^{68} + 12 q^{69} - 8 q^{71} - 12 q^{72} + 24 q^{73} + 32 q^{74} - 32 q^{76} + 56 q^{77} + 40 q^{78} + 20 q^{79} - 14 q^{81} - 4 q^{82} + 26 q^{83} - 12 q^{84} - 36 q^{86} - 8 q^{87} - 72 q^{88} + 12 q^{89} + 26 q^{91} - 22 q^{92} - 88 q^{93} + 18 q^{94} - 46 q^{96} - 42 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(375, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
375.2.g.a 375.g 25.d $4$ $2.994$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(0\) \(0\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{3}+\cdots\)
375.2.g.b 375.g 25.d $8$ $2.994$ 8.0.26265625.1 None \(1\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{3}+\beta _{7})q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{6}+\cdots)q^{3}+\cdots\)
375.2.g.c 375.g 25.d $12$ $2.994$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-3\) \(0\) \(12\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{2}q^{2}+\beta _{8}q^{3}+(-1-\beta _{4}+\beta _{8}+\cdots)q^{4}+\cdots\)
375.2.g.d 375.g 25.d $16$ $2.994$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-2\) \(4\) \(0\) \(16\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{5}q^{2}+\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots\)
375.2.g.e 375.g 25.d $16$ $2.994$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(2\) \(-4\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(\beta _{8}-\beta _{11})q^{4}+(1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(375, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(375, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 2}\)