Properties

Label 1575.2.bc
Level 1575
Weight 2
Character orbit bc
Rep. character \(\chi_{1575}(899,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 5
Sturm bound 480
Trace bound 11

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Defining parameters

Level: \( N \) = \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1575.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 528 96 432
Cusp forms 432 96 336
Eisenstein series 96 0 96

Trace form

\( 96q - 48q^{4} + O(q^{10}) \) \( 96q - 48q^{4} - 48q^{16} - 12q^{19} + 24q^{31} + 24q^{46} - 12q^{49} - 12q^{61} + 96q^{64} - 24q^{79} + 12q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1575.2.bc.a \(8\) \(12.576\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+(3\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
1575.2.bc.b \(8\) \(12.576\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+2\zeta_{24}^{2}q^{4}+(2\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{5}q^{11}+\cdots\)
1575.2.bc.c \(24\) \(12.576\) None \(0\) \(0\) \(0\) \(0\)
1575.2.bc.d \(24\) \(12.576\) None \(0\) \(0\) \(0\) \(0\)
1575.2.bc.e \(32\) \(12.576\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T^{2} )^{4}( 1 + 2 T^{2} + 4 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 4 T^{4} )^{4} \))
$3$ 1
$5$ 1
$7$ (\( ( 1 - 13 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 49 T^{4} )^{2} \))
$11$ (\( ( 1 + 20 T^{2} + 279 T^{4} + 2420 T^{6} + 14641 T^{8} )^{2} \))(\( ( 1 + 4 T^{2} - 105 T^{4} + 484 T^{6} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 - T^{2} + 169 T^{4} )^{4} \))(\( ( 1 + 14 T^{2} + 169 T^{4} )^{4} \))
$17$ (\( ( 1 + 10 T^{2} - 189 T^{4} + 2890 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 20 T^{2} + 111 T^{4} - 5780 T^{6} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} )^{4} \))(\( ( 1 + 12 T + 67 T^{2} + 228 T^{3} + 361 T^{4} )^{4} \))
$23$ (\( ( 1 - 14 T^{2} - 333 T^{4} - 7406 T^{6} + 279841 T^{8} )^{2} \))(\( ( 1 + 26 T^{2} + 147 T^{4} + 13754 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 - 50 T^{2} + 841 T^{4} )^{4} \))(\( ( 1 + 14 T^{2} + 841 T^{4} )^{4} \))
$31$ (\( ( 1 - 7 T + 31 T^{2} )^{4}( 1 + 4 T + 31 T^{2} )^{4} \))(\( ( 1 - 9 T + 58 T^{2} - 279 T^{3} + 961 T^{4} )^{4} \))
$37$ (\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2}( 1 + 47 T^{2} + 1369 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1369 T^{4} )^{2}( 1 + 47 T^{2} + 1369 T^{4} )^{2} \))
$41$ (\( ( 1 + 28 T^{2} + 1681 T^{4} )^{4} \))(\( ( 1 + 28 T^{2} + 1681 T^{4} )^{4} \))
$43$ (\( ( 1 - 85 T^{2} + 1849 T^{4} )^{4} \))(\( ( 1 - 85 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 - 56 T^{2} + 927 T^{4} - 123704 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 + 40 T^{2} - 609 T^{4} + 88360 T^{6} + 4879681 T^{8} )^{2} \))
$53$ (\( ( 1 - 98 T^{2} + 6795 T^{4} - 275282 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 - 88 T^{2} + 4935 T^{4} - 247192 T^{6} + 7890481 T^{8} )^{2} \))
$59$ (\( ( 1 - 94 T^{2} + 5355 T^{4} - 327214 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 64 T^{2} + 615 T^{4} - 222784 T^{6} + 12117361 T^{8} )^{2} \))
$61$ (\( ( 1 + 6 T + 73 T^{2} + 366 T^{3} + 3721 T^{4} )^{4} \))(\( ( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} )^{4} \))
$67$ (\( ( 1 - 109 T^{2} + 4489 T^{4} )^{2}( 1 + 122 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 130 T^{2} + 12411 T^{4} + 583570 T^{6} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 - 92 T^{2} + 5041 T^{4} )^{4} \))(\( ( 1 - 124 T^{2} + 5041 T^{4} )^{4} \))
$73$ (\( ( 1 - 97 T^{2} + 5329 T^{4} )^{2}( 1 - 46 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 71 T^{2} - 288 T^{4} - 378359 T^{6} + 28398241 T^{8} )^{2} \))
$79$ (\( ( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} )^{4} \))(\( ( 1 - 4 T + 79 T^{2} )^{4}( 1 + 17 T + 79 T^{2} )^{4} \))
$83$ (\( ( 1 - 112 T^{2} + 6889 T^{4} )^{4} \))(\( ( 1 - 112 T^{2} + 6889 T^{4} )^{4} \))
$89$ (\( ( 1 - 154 T^{2} + 15795 T^{4} - 1219834 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 124 T^{2} + 7455 T^{4} - 982204 T^{6} + 62742241 T^{8} )^{2} \))
$97$ (\( ( 1 + 86 T^{2} + 9409 T^{4} )^{4} \))(\( ( 1 + 191 T^{2} + 9409 T^{4} )^{4} \))
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