Properties

Label 25.4.a
Level 25
Weight 4
Character orbit a
Rep. character \(\chi_{25}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 3
Sturm bound 10
Trace bound 2

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 25.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(10\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(25))\).

Total New Old
Modular forms 11 6 5
Cusp forms 5 3 2
Eisenstein series 6 3 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)Dim.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3q + 4q^{2} - 2q^{3} - 6q^{4} + 6q^{6} - 6q^{7} + 21q^{9} + O(q^{10}) \) \( 3q + 4q^{2} - 2q^{3} - 6q^{4} + 6q^{6} - 6q^{7} + 21q^{9} - 54q^{11} - 16q^{12} + 38q^{13} - 12q^{14} + 18q^{16} - 26q^{17} - 92q^{18} + 30q^{19} + 96q^{21} + 128q^{22} + 78q^{23} - 210q^{24} + 96q^{26} + 100q^{27} - 48q^{28} + 270q^{29} - 24q^{31} - 256q^{32} - 64q^{33} + 78q^{34} - 492q^{36} - 266q^{37} + 400q^{38} - 468q^{39} - 384q^{41} + 48q^{42} - 442q^{43} + 858q^{44} + 636q^{46} + 514q^{47} + 128q^{48} - 921q^{49} + 1326q^{51} + 304q^{52} - 2q^{53} + 330q^{54} - 180q^{56} - 200q^{57} - 200q^{58} - 60q^{59} - 1554q^{61} - 432q^{62} + 138q^{63} - 846q^{64} - 858q^{66} - 126q^{67} - 208q^{68} + 2112q^{69} + 1236q^{71} + 878q^{73} - 1692q^{74} + 1290q^{76} - 192q^{77} - 304q^{78} + 1620q^{79} - 1257q^{81} + 88q^{82} - 282q^{83} - 492q^{84} - 1584q^{86} + 100q^{87} - 2040q^{89} - 564q^{91} + 624q^{92} + 216q^{93} + 2448q^{94} + 2766q^{96} - 386q^{97} - 1228q^{98} - 2628q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5
25.4.a.a \(1\) \(1.475\) \(\Q\) None \(-1\) \(-7\) \(0\) \(-6\) \(-\) \(q-q^{2}-7q^{3}-7q^{4}+7q^{6}-6q^{7}+\cdots\)
25.4.a.b \(1\) \(1.475\) \(\Q\) None \(1\) \(7\) \(0\) \(6\) \(+\) \(q+q^{2}+7q^{3}-7q^{4}+7q^{6}+6q^{7}+\cdots\)
25.4.a.c \(1\) \(1.475\) \(\Q\) None \(4\) \(-2\) \(0\) \(-6\) \(+\) \(q+4q^{2}-2q^{3}+8q^{4}-8q^{6}-6q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 8 T^{2} \))(\( 1 - T + 8 T^{2} \))(\( 1 - 4 T + 8 T^{2} \))
$3$ (\( 1 + 7 T + 27 T^{2} \))(\( 1 - 7 T + 27 T^{2} \))(\( 1 + 2 T + 27 T^{2} \))
$5$ 1
$7$ (\( 1 + 6 T + 343 T^{2} \))(\( 1 - 6 T + 343 T^{2} \))(\( 1 + 6 T + 343 T^{2} \))
$11$ (\( 1 + 43 T + 1331 T^{2} \))(\( 1 + 43 T + 1331 T^{2} \))(\( 1 - 32 T + 1331 T^{2} \))
$13$ (\( 1 - 28 T + 2197 T^{2} \))(\( 1 + 28 T + 2197 T^{2} \))(\( 1 - 38 T + 2197 T^{2} \))
$17$ (\( 1 + 91 T + 4913 T^{2} \))(\( 1 - 91 T + 4913 T^{2} \))(\( 1 + 26 T + 4913 T^{2} \))
$19$ (\( 1 + 35 T + 6859 T^{2} \))(\( 1 + 35 T + 6859 T^{2} \))(\( 1 - 100 T + 6859 T^{2} \))
$23$ (\( 1 + 162 T + 12167 T^{2} \))(\( 1 - 162 T + 12167 T^{2} \))(\( 1 - 78 T + 12167 T^{2} \))
$29$ (\( 1 - 160 T + 24389 T^{2} \))(\( 1 - 160 T + 24389 T^{2} \))(\( 1 + 50 T + 24389 T^{2} \))
$31$ (\( 1 - 42 T + 29791 T^{2} \))(\( 1 - 42 T + 29791 T^{2} \))(\( 1 + 108 T + 29791 T^{2} \))
$37$ (\( 1 - 314 T + 50653 T^{2} \))(\( 1 + 314 T + 50653 T^{2} \))(\( 1 + 266 T + 50653 T^{2} \))
$41$ (\( 1 + 203 T + 68921 T^{2} \))(\( 1 + 203 T + 68921 T^{2} \))(\( 1 - 22 T + 68921 T^{2} \))
$43$ (\( 1 + 92 T + 79507 T^{2} \))(\( 1 - 92 T + 79507 T^{2} \))(\( 1 + 442 T + 79507 T^{2} \))
$47$ (\( 1 + 196 T + 103823 T^{2} \))(\( 1 - 196 T + 103823 T^{2} \))(\( 1 - 514 T + 103823 T^{2} \))
$53$ (\( 1 + 82 T + 148877 T^{2} \))(\( 1 - 82 T + 148877 T^{2} \))(\( 1 + 2 T + 148877 T^{2} \))
$59$ (\( 1 + 280 T + 205379 T^{2} \))(\( 1 + 280 T + 205379 T^{2} \))(\( 1 - 500 T + 205379 T^{2} \))
$61$ (\( 1 + 518 T + 226981 T^{2} \))(\( 1 + 518 T + 226981 T^{2} \))(\( 1 + 518 T + 226981 T^{2} \))
$67$ (\( 1 + 141 T + 300763 T^{2} \))(\( 1 - 141 T + 300763 T^{2} \))(\( 1 + 126 T + 300763 T^{2} \))
$71$ (\( 1 - 412 T + 357911 T^{2} \))(\( 1 - 412 T + 357911 T^{2} \))(\( 1 - 412 T + 357911 T^{2} \))
$73$ (\( 1 - 763 T + 389017 T^{2} \))(\( 1 + 763 T + 389017 T^{2} \))(\( 1 - 878 T + 389017 T^{2} \))
$79$ (\( 1 - 510 T + 493039 T^{2} \))(\( 1 - 510 T + 493039 T^{2} \))(\( 1 - 600 T + 493039 T^{2} \))
$83$ (\( 1 + 777 T + 571787 T^{2} \))(\( 1 - 777 T + 571787 T^{2} \))(\( 1 + 282 T + 571787 T^{2} \))
$89$ (\( 1 + 945 T + 704969 T^{2} \))(\( 1 + 945 T + 704969 T^{2} \))(\( 1 + 150 T + 704969 T^{2} \))
$97$ (\( 1 + 1246 T + 912673 T^{2} \))(\( 1 - 1246 T + 912673 T^{2} \))(\( 1 + 386 T + 912673 T^{2} \))
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